A025979 Expansion of 1/((1-2*x)*(1-4*x)*(1-8*x)*(1-12*x)).

1, 26, 452, 6664, 90384, 1169952, 14730304, 182323328, 2232488192, 27147248128, 328628192256, 3966436411392, 47780455321600, 574831345147904, 6909703728939008, 83010267592032256, 996873802452369408, 11968490394571898880, 143669922993449205760, 1724423382539837112320

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..900

Index entries for linear recurrences with constant coefficients, signature (26,-224,736,-768).

Formula

G.f.: 1/((1-2*x)*(1-4*x)*(1-8*x)*(1-12*x)).

a(n) = -2^n/15 +4^n/1-16*8^n/3+27*12^n/5. - R. J. Mathar, Jun 20 2013

a(n) = (4^(n+1)-2^(n+1))/2+20*a(n-1)-96*a(n-2). - Vincenzo Librandi, Jun 30 2026

Mathematica

a[0]=1; a[1]=26; Do[a[n]=(4^(n+1)-2^(n+1))/2+20*a[n-1]-96*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 19}] (* Vincenzo Librandi, Jun 30 2026 *)

Prog

(Magma) I:=[1, 26]; [n le 2 select I[n] else (4^n-2^n)/2+20*Self(n-1)-96*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 30 2026

Crossrefs

Sequence in context: A025981 A025996 A023540 * A020970 A023953 A020968

Adjacent sequences: A025976 A025977 A025978 * A025980 A025981 A025982

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 30 2026

Status

approved