A019869 Expansion of 1/((1-5*x)*(1-6*x)*(1-12*x)).

1, 23, 367, 5075, 65551, 817643, 10013527, 121451315, 1465540351, 17637184763, 211960186087, 2545454874755, 30557298487951, 366759842503883, 4401557777453047, 52821361851453395, 633872505937432351

Offset

0,2

Comments

a(n) is the number of partitions of n into parts 5, 6, and 12. - Joerg Arndt, Apr 29 2017

Links

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

Index entries for linear recurrences with constant coefficients, signature (23,-162,360).

Formula

G.f.: 1/((1-5*x)*(1-6*x)*(1-12*x)).

a(n) = 25*5^n/7-6*6^n+24*12^n/7. - R. J. Mathar, Jun 29 2013

a(0)=1, a(1)=23, a(2)=367; for n>2, a(n) = 23*a(n-1) -162*a(n-2) +360*a(n-3). - Vincenzo Librandi, Jul 03 2013

a(n) = 18*a(n-1) -72*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013

Maple

A019869:=n->25*5^n/7-6*6^n+24*12^n/7: seq(A019869(n), n=0..25); # Wesley Ivan Hurt, Apr 28 2017

Mathematica

CoefficientList[Series[1 / ((1 - 5 x) (1 - 6 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{23, -162, 360}, {1, 23, 367}, 20] (* Harvey P. Dale, Aug 04 2020 *)

Prog

(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-6*x)*(1-12*x)))); /* or */ I:=[1, 23, 367]; [n le 3 select I[n] else 23*Self(n-1)-162*Self(n-2)+360*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 2013

Crossrefs

Sequence in context: A021844 A019672 A021629 * A021294 A019628 A018091

Adjacent sequences: A019866 A019867 A019868 * A019870 A019871 A019872

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved