A025964 Expansion of 1/((1-2*x)*(1-4*x)*(1-5*x)*(1-12*x)).

1, 23, 359, 4843, 61287, 753315, 9137263, 110167211, 1324737623, 15911030707, 191005360767, 2292437677179, 27511152416359, 330143464656899, 3961770291040271, 47541489215721547, 570499107794719095, 6845995513926539091, 82151977406506710175, 985823885624777017115

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-170,496,-480).

Formula

G.f.: 1/((1-2*x)*(1-4*x)*(1-5*x)*(1-12*x)).

a(0)=1, a(1)=23, a(2)=359, a(3)=4843, a(n) = 23*a(n-1)-170*a(n-2)+496*a(n-3)-480*a(n-4). - Harvey P. Dale, Jan 28 2013

a(n) = (3*12^(n+3)-80*5^(n+3)+105*4^(n+3)-28*2^(n+3))/1680. - Yahia Kahloune, May 23 2013

a(n) = (4^(n+1)-2^(n+1))/2+17*a(n-1)-60*a(n-2). - Vincenzo Librandi, Jun 04 2026

Mathematica

CoefficientList[Series[1/((1-2*x)*(1-4*x)*(1-5*x)*(1-12*x)), {x, 0, 30}], x](* Harvey P. Dale, Jan 28 2013 *)
(* Alternative: *)
LinearRecurrence[{23, -170, 496, -480}, {1, 23, 359, 4843}, 30] (* Harvey P. Dale, Jan 28 2013 *)
(* Alternative: *)
a[0]=1; a[1]=23; Do[a[n]=(4^(n+1)-2^(n+1))/2+17*a[n-1]-60*a[n-2], {n, 2, 22}]; Table[a[n], {n, 0, 19}] (* Vincenzo Librandi, Jun 04 2026 *)

Prog

(Magma) I:=[1, 23]; [n le 2 select I[n] else (4^n-2^n)/2+17*Self(n-1)-60*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Jun 04 2026

Crossrefs

Sequence in context: A021884 A101792 A020346 * A180361 A021684 A138578

Adjacent sequences: A025961 A025962 A025963 * A025965 A025966 A025967

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Extensions

More terms from Vincenzo Librandi, Jun 04 2026

Status

approved