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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Edward Porcella

Edward Porcella's wiki page.

Edward Porcella has authored 1 sequences.

A341441 Total number of triangles visible in a regular (2n+1)-gon with all diagonals drawn.

Original entry on oeis.org

1, 35, 287, 1302, 4257, 11297, 25935, 53516, 101745, 181279, 306383, 495650, 772785, 1167453, 1716191, 2463384, 3462305, 4776219, 6479551, 8659118, 11415425, 14864025, 19136943, 24384164, 30775185, 38500631, 47773935, 58833082, 71942417, 87394517, 105512127
Offset: 1

Author

Edward Porcella, Feb 11 2021

Keywords

Comments

For n=1, an equilateral triangle, there is no diagonal, and thus the polygon itself is the only triangle.

Crossrefs

Bisection (odd part) of A005732 and of A006600.

Formula

a(n) = n*(2*n+1)*(2*n-1)*(2*n^3+21*n^2-2*n+9)/90.
G.f.: x*(x^5+20*x^4+7*x^3-63*x^2-28*x-1)/(x-1)^7. - Alois P. Heinz, Feb 11 2021
E.g.f.: exp(x)*x*(90 + 1485*x + 2775*x^2 + 1350*x^3 + 204*x^4 + 8*x^5)/90. - Stefano Spezia, Feb 12 2021