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 A308124 a(n) = (2 + 7*4^n)/3. 1
 3, 10, 38, 150, 598, 2390, 9558, 38230, 152918, 611670, 2446678, 9786710, 39146838, 156587350, 626349398, 2505397590, 10021590358, 40086361430, 160345445718, 641381782870, 2565527131478, 10262108525910, 41048434103638, 164193736414550, 656774945658198, 2627099782632790 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Consider A092808 and its differences: 1, 0, 3, 1, 11, 5, 43, 21, 171, ... -1, 3, -2, 10, -6, 38, -22, 150, ... = b(n). a(n) is the second bisection of b(n). The first is A047849. a(n) mod 9 is the period 9 sequence: repeat {3, 1, 2, 6, 4, 5, 0, 7, 8]. b(n) + b(n+1) = A135520{n). LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (5,-4). FORMULA a(n) = 4*a(n-1) - 2 for n=1,2,... , a(0) = 3. a(n+1) = a(n) + A002042(n). Binomial transform of A141495(n+1) = 3, 7, 21, .... From Colin Barker, Jul 23 2019: (Start) G.f.: (3 - 5*x) / ((1 - x)*(1 - 4*x)). a(n) = 5*a(n-1) - 4*a(n-2) for n>1. (End) a(n+2) = a(n) + 35*A000302(n) for n=0,1,2, ... . MATHEMATICA LinearRecurrence[{5, -4}, {3, 10}, 30] (* Paolo Xausa, Nov 13 2023 *) PROG (PARI) a(n) = (2 + 7*4^n)/3; \\ Stefano Spezia, Jul 23 2019 (PARI) Vec((3 - 5*x) / ((1 - x)*(1 - 4*x)) + O(x^40)) \\ Colin Barker, Jul 23 2019 CROSSREFS Cf. A000302, A001045, A002042, A092808, A047849, A135520, A141495. Sequence in context: A149047 A196469 A083692 * A151059 A151060 A151061 Adjacent sequences: A308121 A308122 A308123 * A308125 A308126 A308127 KEYWORD nonn,easy AUTHOR Paul Curtz, Jul 23 2019 EXTENSIONS a(14)-a(25) from Stefano Spezia, Jul 23 2019 STATUS approved

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Last modified April 16 03:20 EDT 2024. Contains 371696 sequences. (Running on oeis4.)