A365934 Number of 4-cycles in the n-Sierpinski carpet graph.

0, 16, 192, 1744, 14592, 118672, 955200, 7659088, 61325184, 490758928, 3926543808, 31413767632, 251314392576, 2010527895184, 16084261425216, 128674206192976, 1029393993917568, 8235152984461840, 65881226975058624, 527049825098560720, 4216398628682760960

Offset

1,2

Links

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

Eric Weisstein's World of Mathematics, Graph Cycle.

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

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

Formula

a(n) = 8/35*(5 + 2^(1 + 3*n) - 7*3^n).

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

G.f.: -16*x^2/((-1+x)*(-1+3*x)*(-1+8*x)).

a(n) = 16*A016214(n-2). - R. J. Mathar, Feb 18 2024

Mathematica

Table[8/35 (5 + 2^(1 + 3 n) - 7 3^n), {n, 20}]
LinearRecurrence[{12, -35, 24}, {0, 16, 192}, 20]
CoefficientList[Series[-16 x/((-1 + x) (-1 + 3 x) (-1 + 8 x)), {x, 0, 20}], x]

Crossrefs

Sequence in context: A305590 A232426 A317008 * A316873 A071081 A317601

Adjacent sequences: A365931 A365932 A365933 * A365935 A365936 A365937

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 07 2023

Status

approved