A394279 - OEIS

%I #4 Mar 14 2026 17:16:05

%S 1,3,11,25,54,98,170,270,415,605,861,1183,1596,2100,2724,3468,4365,

%T 5415,6655,8085,9746,11638,13806,16250,19019,22113,25585,29435,33720,

%U 38440,43656,49368,55641,62475,69939,78033,86830,96330,106610,117670,129591,142373

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BlackBishopGraph.html">Black Bishop Graph</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CubePolynomial.html">Cube Polynomial</a>.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-5,5,1,-3,1).

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

%F 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).

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

%t Table[(n + 1) (3 - 3 (-1)^n + n (n + 1) (n + 2))/24, {n, 20}]

%t LinearRecurrence[{3, -1, -5, 5, 1, -3, 1}, {1, 3, 11, 25, 54, 98, 170}, 20]

%t CoefficientList[Series[(-1 - 3 x^2)/((-1 + x)^5 (1 + x)^2), {x, 0, 20}], x]

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Mar 14 2026