OFFSET
1,3
LINKS
Eric Weisstein's World of Mathematics, Black Bishop Graph.
Eric Weisstein's World of Mathematics, Detour Index.
Index entries for linear recurrences with constant coefficients, signature (2,4,-10,-5,20,0,-20,5,10,-4,-2,1).
FORMULA
a(n) = (2*n^2 - 3 - (-1)^n)^2*(2*n^2 + 1 - (-1)^n)/128.
a(n) = (3*n^2 - 5*n^4 + 2*n^6 + 1 + (-1)^n*(5*n^2 - 3*n^4 - 1))/32.
a(n) = 2*a(n-1)+4*a(n-2)-10*a(n-3)-5*a(n-4)+20*a(n-5)-20*a(n-7)+5*a(n-8)+10*a(n-9)-4*a(n-10)-2*a(n-11)+a(n-12).
G.f.: x^2*(-1-38*x-112*x^2-394*x^3-350*x^4-394*x^5-112*x^6-38*x^7-x^8)/((-1+x)^7*(1+x)^5).
MATHEMATICA
Table[(2 n^2 - 3 - (-1)^n)^2 (2 n^2 + 1 - (-1)^n)/128, {n, 20}]
Table[(3 n^2 - 5 n^4 + 2 n^6 + 1 + (-1)^n (5 n^2 - 3 n^4 - 1))/32, {n, 20}]
LinearRecurrence[{2, 4, -10, -5, 20, 0, -20, 5, 10, -4, -2, 1}, {0, 1, 40, 196, 936, 2601, 7200, 15376, 32800, 60025, 109800, 181476}, 20]
CoefficientList[Series[x (-1 - 38 x - 112 x^2 - 394 x^3 - 350 x^4 - 394 x^5 - 112 x^6 - 38 x^7 - x^8)/((-1 + x)^7 (1 + x)^5), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Sep 04 2025
STATUS
approved