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 A283070 Sierpinski tetrahedron or tetrix numbers: a(n) = 2*4^n + 2. 3
 4, 10, 34, 130, 514, 2050, 8194, 32770, 131074, 524290, 2097154, 8388610, 33554434, 134217730, 536870914, 2147483650, 8589934594, 34359738370, 137438953474, 549755813890, 2199023255554, 8796093022210, 35184372088834, 140737488355330, 562949953421314 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Number of vertices required to make a Sierpinski tetrahedron or tetrix of side length 2^n. The sum of the vertices (balls) plus line segments (rods) of one tetrix equals the vertices of its larger, adjacent iteration. See formula. Equivalently, the number of vertices in the (n+1)-Sierpinski tetrahedron graph. - Eric W. Weisstein, Aug 17 2017 Final digit alternates 4 and 0. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Sierpinski Tetrahedron Graph Eric Weisstein's World of Mathematics, Tetrix Eric Weisstein's World of Mathematics, Vertex Count Index entries for linear recurrences with constant coefficients, signature (5,-4). FORMULA G.f.: 2*(2 - 5*x)/((1 - x)*(1 - 4*x)). a(n) = 5*a(n-1) - 4*a(n-2) for n > 1. a(n+1) = a(n) + A002023(n). a(n) = 2*A052539(n) = A188161(n) - 1 = A087289(n) + 1 = A056469(2*n+2) = A261723(4*n+1). E.g.f.: 2*(exp(4*x) + exp(x)). - G. C. Greubel, Aug 17 2017 MATHEMATICA Table[2 4^n + 2, {n, 0, 30}] (* Bruno Berselli, Feb 28 2017 *) 2 (4^Range[0, 20] + 1) (* Eric W. Weisstein, Aug 17 2017 *) LinearRecurrence[{5, -4}, {4, 10}, 20] (* Eric W. Weisstein, Aug 17 2017 *) CoefficientList[Series[-((2 (-2 + 5 x))/(1 - 5 x + 4 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Aug 17 2017 *) PROG (PARI) a(n)=2*4^n+2 \\ Charles R Greathouse IV, Feb 28 2017 (PARI) Vec(2*(2 - 5*x) / ((1 - x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Mar 02 2017 CROSSREFS Subsequence of A016957. Cf. A052539, A279511, A279512. First bisection of A052548, A087288; second bisection of A049332, A133140, A135440. Cf. A002023 (edge count). Sequence in context: A006343 A149173 A149174 * A222631 A030003 A234009 Adjacent sequences:  A283067 A283068 A283069 * A283071 A283072 A283073 KEYWORD nonn,easy AUTHOR Peter M. Chema, Feb 28 2017 EXTENSIONS Entry revised by Editors of OEIS, Mar 01 2017 STATUS approved

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Last modified November 15 19:54 EST 2018. Contains 317240 sequences. (Running on oeis4.)