A394279 Number of induced cubes in the n X n black bishop graph.

1, 3, 11, 25, 54, 98, 170, 270, 415, 605, 861, 1183, 1596, 2100, 2724, 3468, 4365, 5415, 6655, 8085, 9746, 11638, 13806, 16250, 19019, 22113, 25585, 29435, 33720, 38440, 43656, 49368, 55641, 62475, 69939, 78033, 86830, 96330, 106610, 117670, 129591, 142373

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Eric Weisstein's World of Mathematics, Black Bishop Graph.

Eric Weisstein's World of Mathematics, Cube Polynomial.

Index entries for linear recurrences with constant coefficients, signature (3,-1,-5,5,1,-3,1).

Formula

a(n) = (n + 1)*(3 - 3*(-1)^n + n*(n + 1)*(n + 2))/24.

a(n) = 3*a(n-1)-a(n-2)-5*a(n-3)+5*a(n-4)+a(n-5)-3*a(n-6)+a(n-7).

G.f.: x*(-1-3*x^2)/((-1+x)^5*(1+x)^2).

Mathematica

Table[(n + 1) (3 - 3 (-1)^n + n (n + 1) (n + 2))/24, {n, 20}]
LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {1, 3, 11, 25, 54, 98, 170}, 20]
CoefficientList[Series[(-1 - 3 x^2)/((-1 + x)^5 (1 + x)^2), {x, 0, 20}], x]

Crossrefs

Sequence in context: A212971 A258440 A184634 * A352013 A164303 A129082

Adjacent sequences: A394276 A394277 A394278 * A394280 A394281 A394282

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 14 2026

Status

approved