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 A323824 a(0) = 6; thereafter a(n) = 4*a(n-1) + 1. 2
 6, 25, 101, 405, 1621, 6485, 25941, 103765, 415061, 1660245, 6640981, 26563925, 106255701, 425022805, 1700091221, 6800364885, 27201459541, 108805838165, 435223352661, 1740893410645, 6963573642581, 27854294570325, 111417178281301, 445668713125205 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Mike Warburton, Ulam-Warburton Automaton - Counting Cells with Quadratics, arXiv:1901.10565 [math.CO], 2019. Index entries for linear recurrences with constant coefficients, signature (5,-4). FORMULA G.f.: (6 - 5*x) / ((1 - x)*(1 - 4*x)). a(n) = (19*4^n - 1) / 3. - Colin Barker, Feb 01 2019 a(n) = A178415(7, n) = A347834(10, n-1), arrays, for n >= 1. - Wolfdieter Lang, Nov 29 2021 PROG (PARI) Vec((6 - 5*x) / ((1 - x)*(1 - 4*x)) + O(x^25)) \\ Colin Barker, Feb 01 2019 (PARI) a(n) = (19*4^n - 1) / 3 \\ Colin Barker, Feb 01 2019 CROSSREFS Cf. A178415, A347834. Sequence in context: A009121 A327504 A346390 * A037537 A253220 A037481 Adjacent sequences:  A323821 A323822 A323823 * A323825 A323826 A323827 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Feb 01 2019 STATUS approved

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Last modified January 26 22:05 EST 2022. Contains 350601 sequences. (Running on oeis4.)