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A323824
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a(0) = 6; thereafter a(n) = 4*a(n-1) + 1.
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2
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6, 25, 101, 405, 1621, 6485, 25941, 103765, 415061, 1660245, 6640981, 26563925, 106255701, 425022805, 1700091221, 6800364885, 27201459541, 108805838165, 435223352661, 1740893410645, 6963573642581, 27854294570325, 111417178281301, 445668713125205
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OFFSET
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0,1
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LINKS
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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).
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FORMULA
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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
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PROG
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(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
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CROSSREFS
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Cf. A178415, A347834.
Sequence in context: A009121 A327504 A346390 * A037537 A253220 A037481
Adjacent sequences: A323821 A323822 A323823 * A323825 A323826 A323827
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Feb 01 2019
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STATUS
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approved
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