A037489 Base 4 digits are, in order, the first n terms of the periodic sequence with initial period 2,1.

2, 9, 38, 153, 614, 2457, 9830, 39321, 157286, 629145, 2516582, 10066329, 40265318, 161061273, 644245094, 2576980377, 10307921510, 41231686041, 164926744166, 659706976665, 2638827906662, 10555311626649, 42221246506598, 168884986026393, 675539944105574, 2702159776422297

Offset

1,1

Links

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

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

Formula

a(n) = 4a(n-1) + a(n-2) - 4a(n-3).

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

a(n) = floor(3*4^n/5). - Christian Krause, May 30 2026

E.g.f.: (3*(cosh(4*x) - cosh(x) + sinh(4*x)) - 2*sinh(x))/5. - Stefano Spezia, May 31 2026

Mathematica

LinearRecurrence[{4, 1, -4}, {2, 9, 38}, 40] (* Vincenzo Librandi, Jun 22 2012 *)

Prog

(Magma) I:=[2, 9, 38]; [n le 3 select I[n] else 4*Self(n-1)+Self(n-2)-4*Self(n-3): n in [1..30]]; // Vincenzo Librandi, Jun 22 2012

Crossrefs

Sequence in context: A007224 A181339 A291265 * A037569 A291462 A001077

Adjacent sequences: A037486 A037487 A037488 * A037490 A037491 A037492

Keyword

nonn,base,easy,changed

Author

Clark Kimberling

Status

approved