A120662 Expansion of x*(12 +101*x -189*x^2)/((1+2*x)*(1-3*x)*(1-5*x)).

0, 12, 173, 861, 4979, 25545, 132419, 670689, 3390203, 17039337, 85505555, 428366577, 2144524907, 10730349369, 53675623811, 268448345025, 1342455212891, 6712910908041, 33566470310387, 167838076383633

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,1,-30).

Formula

From Colin Barker, Nov 01 2012: (Start)

a(n) = 6*a(n-1) + a(n-2) - 30*a(n-3) for n>3.

G.f.: x*(12 +101*x -189*x^2)/((1+2*x)*(1-3*x)*(1-5*x)). (End)

Mathematica

LinearRecurrence[{6, 1, -30}, {0, 12, 173, 861}, 20] (* Harvey P. Dale, Jan 09 2019 *)

Prog

(Magma) I:=[12, 173, 861]; [0] cat [n le 3 select I[n] else 6*Self(n-1) + Self(n-2) -30*Self(n-3): n in [1..31]]; // G. C. Greubel, Dec 25 2022
(SageMath)
@CachedFunction
def a(n): # a = A120662
    if (n<4): return (0, 12, 173, 861)[n]
    else: return 6*a(n-1) + a(n-2) -30*a(n-3)
[a(n) for n in range(41)] # G. C. Greubel, Dec 25 2022

Crossrefs

Sequence in context: A187361 A366235 A239335 * A230815 A099930 A307549

Adjacent sequences: A120659 A120660 A120661 * A120663 A120664 A120665

Keyword

nonn,easy

Author

Roger L. Bagula, Aug 10 2006

Extensions

Edited by N. J. A. Sloane, Jul 13 2007

Meaningful name using g.f. from Joerg Arndt, Dec 26 2022

Status

approved