A394278 Number of induced cubes in the n X n fiveleaper graph.

1, 4, 9, 16, 33, 73, 129, 205, 331, 529, 779, 1097, 1531, 2075, 2716, 3475, 4376, 5399, 6544, 7824, 9232, 10768, 12432, 14224, 16144, 18192, 20368, 22672, 25104, 27664, 30352, 33168, 36112, 39184, 42384, 45712, 49168, 52752, 56464, 60304, 64272, 68368, 72592

Offset

1,2

Links

Table of n, a(n) for n=1..43.

Eric Weisstein's World of Mathematics, Cube Polynomial.

Eric Weisstein's World of Mathematics, Fiveleaper Graph.

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

Formula

a(n) = 16*(409 - 76*n + 4*n^2) for n > 18.

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

G.f.: x*(-1-x-8*x^4-13*x^5+7*x^6-4*x^7-30*x^8-22*x^9+20*x^10-16*x^11-48*x^12+6*x^13+13*x^14-21*x^15-24*x^16+20*x^17-13*x^19+7*x^20)/(-1+x)^3.

Mathematica

Table[n^2 + Ramp[n - 19]^2 + 4 Ramp[n - 16] Ramp[n - 15] + 2 Ramp[n - 19] Ramp[n - 14] + Ramp[n - 14]^2 + 4 Ramp[n - 12]^2 + 4 Ramp[n - 15] Ramp[n - 11] + 2 Ramp[n - 13] Ramp[n - 11] + 4 Ramp[n - 16] Ramp[n - 10] + 4 Ramp[n - 11] Ramp[n - 10] + 2 Ramp[n - 11] Ramp[n - 8] + 4 Ramp[n - 9] Ramp[n - 8] + 8 Ramp[n - 12] Ramp[n - 7] + 4 Ramp[n - 7]^2 + 2 Ramp[n - 13] Ramp[n - 6] + 2 Ramp[n - 8] Ramp[n - 6] + 2 n Ramp[n - 5] + Ramp[n - 5]^2 + 4 Ramp[n - 8] Ramp[n - 4] + 4 Ramp[n - 9] Ramp[n - 3] + 4 Ramp[n - 4] Ramp[n - 3], {n, 20}]
Join[{1, 4, 9, 16, 33, 73, 129, 205, 331, 529, 779, 1097, 1531, 2075, 2716, 3475, 4376, 5399}, LinearRecurrence[{3, -3, 1}, {6544, 7824, 9232}, 2]]
CoefficientList[Series[(-1 - x - 8 x^4 - 13 x^5 + 7 x^6 - 4 x^7 - 30 x^8 - 22 x^9 + 20 x^10 - 16 x^11 - 48 x^12 + 6 x^13 + 13 x^14 - 21 x^15 - 24 x^16 + 20 x^17 - 13 x^19 + 7 x^20)/(-1 + x)^3, {x, 0, 20}], x]

Crossrefs

Sequence in context: A167188 A295720 A349800 * A296152 A354840 A014764

Adjacent sequences: A394275 A394276 A394277 * A394279 A394280 A394281

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 14 2026

Status

approved