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 A295933 Number of (not necessarily maximum) cliques in the n-Sierpinski sieve graph. 1
 8, 20, 55, 160, 475, 1420, 4255, 12760, 38275, 114820, 344455, 1033360, 3100075, 9300220, 27900655, 83701960, 251105875, 753317620, 2259952855, 6779858560, 20339575675, 61018727020, 183056181055, 549168543160, 1647505629475, 4942516888420, 14827550665255 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Clique Eric Weisstein's World of Mathematics, Sierpinski Sieve Graph Index entries for linear recurrences with constant coefficients, signature (4, -3). FORMULA a(n) = 5*(3 + 7*3^(n - 1))/6 for n > 1. a(n) = 4*a(n-1) - 3*a(n-2) for n > 1. G.f.: x*(8 - 12*x - x^2)/(1 - 4*x + 3*x^2). E.g.f.: (-80 - 6*x + 45*exp(x) + 35*exp(3*x))/18. - G. C. Greubel, May 21 2019 MATHEMATICA Table[If[n == 1, 8, 5*(3 + 7*3^(n-1))/6], {n, 30}] Join[{8}, LinearRecurrence[{4, -3}, {20, 55}, 30]] CoefficientList[Series[(8 -12x -x^2)/(1 -4x +3x^2), {x, 0, 30}], x] PROG (PARI) {a(n) = if(n==1, 8, 5*(1 +7*3^(n-2))/2)}; \\ G. C. Greubel, May 21 2019 (Magma) [n eq 1 select 8 else 5*(1 +7*3^(n-2))/2: n in [1..30]]; // G. C. Greubel, May 21 2019 (Sage) [8] + [5*(1 +7*3^(n-2))/2 for n in (2..30)] # G. C. Greubel, May 21 2019 (GAP) Concatenation([8], List([2..30], n-> 5*(1 +7*3^(n-2))/2 )) # G. C. Greubel, May 21 2019 CROSSREFS Sequence in context: A205219 A232401 A036835 * A212758 A179756 A238507 Adjacent sequences: A295930 A295931 A295932 * A295934 A295935 A295936 KEYWORD nonn,easy AUTHOR Eric W. Weisstein, Nov 29 2017 STATUS approved

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)