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

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

1,2

Comments

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

Links

Table of n, a(n) for n=1..31.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

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

Crossrefs

Bisection (odd part) of A005732 and of A006600.

Sequence in context: A219575 A219711 A055658 * A125773 A198397 A071697

Adjacent sequences: A341438 A341439 A341440 * A341442 A341443 A341444

Keyword

nonn,easy

Author

Edward Porcella, Feb 11 2021

Status

approved