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# MY CONTRIBUTIONS

- A350116 – Number of ways to partition the set of vertices of a convex (n +8) – gon into 3 nonintersecting polygons.
- A350248 – Triangle read by rows T(n,k) is the number of noncrossing partitions of an n – set into k blocks of size 3 or more, n > = 0, 0 < = k < = floor (n/3)
- A350286 – Number of different ways to partition the set of vertices of a convex (n + 11) – gon into 4 nonintersecting polygons.
- A350303 – Number of ways to partition the set of vertices of a convex (n + 14) – gon into 5 nonintersecting polygons.
- A350599 – Number of ways to partition the set of vertices of a convex n – gon into nonintersecting directed polygons.
- A350640 – Minimum lcm of the part sizes of a partition of n into parts of size 3 or more.
- A347862 – Total number of polygons left out in all partitions of the set of vertices of a convex n – gon into nonintersecting polygons.
- A351103 – Total number of polygons left over with maximum number of sides when partitioning the set of vertices of a convex n – gon into nonintersecting polygons.
- A352477 – Number of different ways to partition the set of vertices of a convex n – gon into 4 intersecting polygons.
- A352474 – Number of different ways to partition the set of vertices of a convex n – gon into 3 intersecting polygons.
- A352611 – Number of different ways to partition the set of vertices of a convex n – gon into 5 polygons.
- A352900 – Number of different ways to partition the set of vertices of a convex n – gon into intersecting polygons.
- A357603 – Number of different pairs of shortest paths in an n X n lattice going between opposite corners in opposite direction and not meeting at their middle point.
- A357760 – Number of different pairs of shortest grid paths joining two opposite corners in opposite order in an n X n X n grid with middle point on the paths as a common point.
- A358481 – Number of different pairs of shortest grid paths joining two opposite corners in opposite order in an n X n X n grid without having middle point on their paths as a common point.
- A362207 – Number of unordered triples of shortest nonintersecting grid paths joining two opposite corners of an n X n X n grid.
- A360444 – Number of ways for two nonintersecting, unordered pairs of shortest grid paths to cross over between two opposite corners in an n X n grid without intersecting opposite paths at their middle points.
- Mathematical Model of the sequence A360444.
- Python Code of the Mathematical Model of A360444.
- Mathematical Model of ordered triplets ( An open challenge to create a computer program and obtain integer outputs)

## New proofs and totally different approaches in other fields of mathematics

- Geometrical proof of the sum of infinite series Cot
^{-1}3 + Cot^{-1}7 + Cot^{-1}13 + …….. converges to π /4.

- Geometrical proof of the sum of infinite series Cot
^{-1}2 + Cot^{-1}8 + Cot^{-1}18 + …….. converges to π /4. - Geometrical proof of the sum of infinite series 1/1.2 + 1/2.3 + 1/3.4 + …… converges to 1.
- Geometrical proof of sum and the product of three tangents of a triangle are equal in the case of an obtuse-angled triangles.
- The Inclusion-Exclusion Principle in geometrical approach of completing square in Quadratics.
- Fully trigonometric proof of Pythagoras theorem without applying properties of similar triangles.
- Simultaneous Single Proof of the Sine Law and Cosine Law.