A020569 Expansion of g.f. 1/((1 - 5*x)*(1 - 11*x)*(1 - 12*x)).

1, 28, 537, 8780, 131681, 1872828, 25708777, 344166700, 4522666161, 58593270428, 750663052217, 9530987332620, 120125429898241, 1504795780456828, 18753752307454857, 232703290568738540, 2876680531084835921, 35446818622817192028, 435555002036294340697, 5338785007696386816460

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (28,-247,660).

Formula

a(n) = 25*5^n/42 -121*11^n/6 +144*12^n/7. - R. J. Mathar, Jun 30 2013

a(0)=1, a(1)=28, a(2)=537; for n>2, a(n) = 28*a(n-1) -247*a(n-2) +660*a(n-3). - Vincenzo Librandi, Jul 04 2013

a(n) = 23*a(n-1) -132*a(n-2) +5^n. - Vincenzo Librandi, Jul 04 2013

E.g.f.: exp(5*x)*(25 - 847*exp(6*x) + 864*exp(7*x))/42. - Stefano Spezia, Mar 09 2026

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 11 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 04 2013 *)
LinearRecurrence[{28, -247, 660}, {1, 28, 537}, 20] (* Harvey P. Dale, Dec 25 2013 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-11*x)*(1-12*x)))); // Vincenzo Librandi, Jul 04 2013
(Magma) I:=[1, 28, 537]; [n le 3 select I[n] else 28*Self(n-1)-247*Self(n-2)+660*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 04 2013

Crossrefs

Sequence in context: A020758 A022000 A387311 * A163195 A092708 A163198

Adjacent sequences: A020566 A020567 A020568 * A020570 A020571 A020572

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved