A341441 - OEIS

%I #23 Feb 12 2021 18:53:19

%S 1,35,287,1302,4257,11297,25935,53516,101745,181279,306383,495650,

%T 772785,1167453,1716191,2463384,3462305,4776219,6479551,8659118,

%U 11415425,14864025,19136943,24384164,30775185,38500631,47773935,58833082,71942417,87394517,105512127

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

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

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = n*(2*n+1)*(2*n-1)*(2*n^3+21*n^2-2*n+9)/90.

%F 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

%F 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

%Y Bisection (odd part) of A005732 and of A006600.

%K nonn,easy

%O 1,2

%A _Edward Porcella_, Feb 11 2021