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 A141844 Expansion of (1+x)*(1+x^2)/((1-x)^2*(1+x+x^2)*(1-4*x)). 1
 1, 6, 27, 113, 458, 1839, 7365, 29470, 117891, 471577, 1886322, 7545303, 30181229, 120724934, 482899755, 1931599041, 7726396186, 30905584767, 123622339093, 494489356398, 1977957425619, 7911829702505, 31647318810050, 126589275240231, 506357100960957 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Old name was: a(n) = 4*a(n-1) + A042968(n), with a(0) = 1, where A042968 = "not divisible by 4": (1, 2, 3, 5, 6, 7, 9, 10, 11, ...).  After the correction of a(13) the definition could be simplified. - N. J. A. Sloane, Aug 23 2018 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..1660 Index entries for linear recurrences with constant coefficients, signature (5, -4, 1, -5, 4). FORMULA a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3) - 5*a(n-4) + 4*a(n-5) for n>4. - Colin Barker, Jun 26 2017 EXAMPLE a(3) = 4*a(2) + A042968(3) = 4*27 + 5 = 113. a(13) = 4*a(12) + A042968(13) = 4*30181229 + 18 = 120724934. MATHEMATICA CoefficientList[Series[(1 + x) (1 + x^2) / ((1 - x)^2 (1 + x + x^2) (1 - 4 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 28 2017 *) Nest[Append[#, Block[{k = #[[-1, -1]] + 1}, While[Mod[k, 4] == 0, k++]; {4 #[[-1, 1]] + k, k}]] &, {{1, 1}}, 24][[All, 1]] (* Michael De Vlieger, Jun 30 2018 *) LinearRecurrence[{5, -4, 1, -5, 4}, {1, 6, 27, 113, 458}, 25] (* Robert G. Wilson v, Jul 28 2018 *) PROG (PARI) Vec((1 + x)*(1 + x^2) / ((1 - x)^2*(1 - 4*x)*(1 + x + x^2)) + O(x^30)) \\ Colin Barker, Jun 26 2017 (MAGMA) I:=[1, 6, 27, 113, 458]; [n le 5 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3)-5*Self(n-4)+4*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Jun 28 2017, Jul 28 2018 CROSSREFS Cf. A042968. Sequence in context: A198694 A220101 A014825 * A176476 A079742 A291232 Adjacent sequences:  A141841 A141842 A141843 * A141845 A141846 A141847 KEYWORD nonn AUTHOR Gary W. Adamson, Jul 11 2008 EXTENSIONS Corrected by Charlie Neder, Jun 22 2018 Edited by N. J. A. Sloane, Aug 23 2018, merging old entry A288571 with this one. STATUS approved

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Last modified July 28 19:12 EDT 2021. Contains 346335 sequences. (Running on oeis4.)