A025985 Expansion of 1/((1-2*x)*(1-4*x)*(1-11*x)*(1-12*x)).

1, 29, 563, 9241, 138723, 1972833, 27071851, 362271257, 4758885395, 61635081937, 789436108539, 10021208067273, 126282252770467, 1581692483050241, 19709670281308427, 244539010854912889, 3022720781120153139, 37243428567274628145, 457599714076894924315

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (29,-278,976,-1056).

Formula

a(n) = -2*2^n/45+4*4^n/7-1331*11^n/63+108*12^n/5. - R. J. Mathar, Jun 20 2013

a(n) = 29*a(n-1)-278*a(n-2)+976*a(n-3)-1056*a(n-4), a(0)=1, a(1)=29, a(2)=563, a(3)=9241. - Harvey P. Dale, Nov 25 2013

a(n) = (4^(n+1)-2^(n+1))/2+23*a(n-1)-132*a(n-2). - Vincenzo Librandi, Jul 04 2026

Mathematica

CoefficientList[Series[1/((1-2x)(1-4x)(1-11x)(1-12x)), {x, 0, 30}], x] (* Harvey P. Dale, Nov 25 2013 *)
(* Alternative: *)
LinearRecurrence[{29, -278, 976, -1056}, {1, 29, 563, 9241}, 30] (* Harvey P. Dale, Nov 25 2013 *)

Prog

(Magma) I:=[1, 29]; [n le 2 select I[n] else (4^n-2^n)/2+23*Self(n-1)-132*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jul 04 2026

Crossrefs

Sequence in context: A024443 A024435 A020979 * A020978 A023948 A020974

Adjacent sequences: A025982 A025983 A025984 * A025986 A025987 A025988

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jul 04 2026

Status

approved