A025954 Expansion of 1/((1-2*x)*(1-3*x)*(1-9*x)*(1-12*x)).

1, 26, 457, 6854, 94789, 1251002, 16035889, 201651758, 2502830077, 30781099778, 376097622121, 4573691815862, 55428986530165, 670050005786954, 8084719590584353, 97413710820261566, 1172538211571391853, 14102621674798138130, 169520928322212317785, 2036856353891745491270, 24465723172938183251941

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,-219,666,-648).

Formula

a(n) = 26*a(n-1)-219*a(n-2)+666*a(n-3)-648*a(n-4) with a(0)=1, a(1)=26, a(2)=457, a(3)=6854. [Harvey P. Dale, Jan 19 2012]

a(n) = -4*2^n/35+3^n/2-81*9^n/14+32*12^n/5. - R. J. Mathar, Jun 20 2013

a(n) = 3^(n+1)-2^(n+1)+21*a(n-1)-108*a(n-2). - Vincenzo Librandi, May 26 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-3*x)*(1-9*x)*(1-12*x)), {x, 0, 20}], x] (* Harvey P. Dale, Jan 19 2012 *)
(* Alternative: *)
LinearRecurrence[{26, -219, 666, -648}, {1, 26, 457, 6854}, 20] (* Harvey P. Dale, Jan 19 2012 *)
(* Alternative: *)
a[0]=1; a[1]=26; a[n_]:=a[n]=3^(n+1)-2^(n+1)+21*a[n-1]-108*a[n-2]; Table[a[n], {n, 0, 20}] (* Vincenzo Librandi, May 26 2026 *)

Prog

(Magma) I:=[1, 26]; [n le 2 select I[n] else 3^n-2^n+21*Self(n-1)-108*Self(n-2): n in [1..21]]; // Vincenzo Librandi, May 26 2026

Crossrefs

Sequence in context: A022725 A020606 A021984 * A158436 A158431 A158432

Adjacent sequences: A025951 A025952 A025953 * A025955 A025956 A025957

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, May 26 2026

Status

approved