login
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
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
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
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