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
Links
- 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
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