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A341441 Total number of triangles visible in a regular (2n+1)-gon with all diagonals drawn. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 21 06:26 EST 2022. Contains 350473 sequences. (Running on oeis4.)