A394307 Number of induced cubes in the n X n zebra graph.

1, 4, 9, 24, 49, 88, 151, 236, 351, 496, 672, 880, 1120, 1392, 1696, 2032, 2400, 2800, 3232, 3696, 4192, 4720, 5280, 5872, 6496, 7152, 7840, 8560, 9312, 10096, 10912, 11760, 12640, 13552, 14496, 15472, 16480, 17520, 18592, 19696, 20832, 22000, 23200, 24432

Offset

1,2

Links

Table of n, a(n) for n=1..44.

Eric Weisstein's World of Mathematics, Cube Polynomial.

Eric Weisstein's World of Mathematics, Zebra Graph.

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

Formula

a(n)=16*(n^2-10*n+31) for n > 9.

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n > 12.

G.f.: x*(-1-x-8*x^3-4*x^5-10*x^6+2*x^7-8*x^8-x^10-x^11)/(-1+x)^3.

Mathematica

Table[n^2 + Ramp[n - 10]^2 + 4 Ramp[n - 8] Ramp[n - 7] + 4 Ramp[n - 5]^2 + 2 Ramp[n - 6] Ramp[n - 4] + 4 Ramp[n - 3] Ramp[n - 2], {n, 20}]
Join[{1, 4, 9, 24, 49, 88, 151, 236, 351}, LinearRecurrence[{3, -3, 1}, {496, 672, 880}, 11]]
CoefficientList[Series[(-1 - x - 8 x^3 - 4 x^5 - 10 x^6 + 2 x^7 - 8 x^8 - x^10 - x^11)/(-1 + x)^3, {x, 0, 20}], x]

Crossrefs

Sequence in context: A158141 A056575 A056032 * A304908 A127979 A112262

Adjacent sequences: A394304 A394305 A394306 * A394308 A394309 A394310

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 15 2026

Status

approved