A037737 Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 2,1,3,0.

2, 9, 39, 156, 626, 2505, 10023, 40092, 160370, 641481, 2565927, 10263708, 41054834, 164219337, 656877351, 2627509404, 10510037618, 42040150473, 168160601895, 672642407580, 2690569630322, 10762278521289, 43049114085159

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,0,0,1,-4).

Formula

G.f.: x*(2+x+3*x^2) / ( (x-1)*(4*x-1)*(1+x)*(x^2+1) ). - R. J. Mathar, Nov 21 2011

a(n) = 4*a(n-1) + a(n-4) - 4*a(n-5). - Vincenzo Librandi, Jun 17 2012

Mathematica

With[{c=PadLeft[{}, 24, {2, 1, 3, 0}]}, Table[FromDigits[Take[c, n], 4], {n, 24}]] (* Harvey P. Dale, Oct 03 2011 *)
LinearRecurrence[{4, 0, 0, 1, -4}, {2, 9, 39, 156, 626}, 30] (* Vincenzo Librandi, Jun 17 2012 *)

Prog

(Magma)I:=[2, 9, 39, 156, 626]; [n le 5 select I[n] else 4*Self(n-1)+Self(n-4)-4*Self(n-5): n in [1..30]]; // Vincenzo Librandi, Jun 17 2012

Crossrefs

Sequence in context: A278050 A070017 A054129 * A037632 A095939 A361358

Adjacent sequences: A037734 A037735 A037736 * A037738 A037739 A037740

Keyword

nonn,base

Author

Clark Kimberling

Status

approved