A083589 Expansion of 1/((1-4*x)*(1-x^4)).

1, 4, 16, 64, 257, 1028, 4112, 16448, 65793, 263172, 1052688, 4210752, 16843009, 67372036, 269488144, 1077952576, 4311810305, 17247241220, 68988964880, 275955859520, 1103823438081, 4415293752324, 17661175009296, 70644700037184

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(0)=1, a(n) = 4*a(n-1) if n is not a multiple of 4, otherwise a(n) = 4*a(n-1) + 1. - Vincenzo Librandi, Mar 19 2011

a(n) = 4^(n+4)/255 -1/12 +(-1)^n/20 +(-1)^floor(n/2)*A010685(n)/34. - R. J. Mathar, Mar 19 2011

a(0)=1, a(1)=4, a(2)=16, a(3)=64, a(4)=257, a(n) = 4*a(n-1) + a(n-4) - 4*a(n-5). - Harvey P. Dale, Sep 13 2011

a(n) = floor(64*(2^(2*(n+1))+1)/255). - Tani Akinari, Jul 09 2013

Mathematica

CoefficientList[Series[1/((1-4x)(1-x^4)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {4, 0, 0, 1, -4}, {1, 4, 16, 64, 257}, 31] (* Harvey P. Dale, Sep 13 2011 *)

Prog

(PARI) a(n)=(4^(n+4)+64)\255 \\ Charles R Greathouse IV, Jul 09 2013

Crossrefs

Cf. A033139, A000975.

Sequence in context: A083592 A069029 A238940 * A098590 A270560 A071357

Adjacent sequences: A083586 A083587 A083588 * A083590 A083591 A083592

Keyword

easy,nonn

Author

Paul Barry, May 02 2003

Status

approved