A394274 Number of induced cubes in the n-Sierpinski carpet graph.

1, 16, 168, 1480, 12264, 99400, 799080, 6404296, 51269352, 410259784, 3282393192, 26260090312, 210083556840, 1680676957768, 13445441171304, 107563605897928, 860509076765928, 6884073302874952, 55072588489242216, 440580714112665544, 3524645731497507816

Offset

1,2

Comments

Sequence extended to a(0) using the formula.

Links

Table of n, a(n) for n=1..21.

Eric Weisstein's World of Mathematics, Cube Polynomial.

Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph.

Index entries for linear recurrences with constant coefficients, signature (12,-35,24).

Formula

a(n)=(40-112*3^n+107*8^n)/35.

a(n) = 12*a(n-1)-35*a(n-2)+24*a(n-3).

G.f.: (-1-4*x-11*x^2)/(-1+12*x-35*x^2+24*x^3).

Mathematica

Table[(40 - 112 3^n + 107 8^n)/35, {n, 0, 20}]
LinearRecurrence[{12, -35, 24}, {16, 168, 1480}, {0, 20}]
CoefficientList[Series[(-1 - 4 x - 11 x^2)/(-1 + 12 x - 35 x^2 + 24 x^3), {x, 0, 20}], x]

Crossrefs

Sequence in context: A021744 A025445 A022740 * A205247 A067713 A017210

Adjacent sequences: A394271 A394272 A394273 * A394275 A394276 A394277

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 14 2026

Status

approved