A016244 Expansion of 1/((1-x)*(1-6*x)*(1-9*x)).

1, 16, 187, 1942, 19033, 180628, 1681639, 15470674, 141251605, 1283357680, 11622778531, 105040363246, 947975408017, 8547451504972, 77021100541663, 693754126856458, 6247172473597069, 56244864253707304

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (16,-69,54).

Crossrefs

Cf. A003464, A024346, A024347.

Programs

Magma

[(1 -96*6^n +135*9^n)/40: n in [0..40]]; // G. C. Greubel, Jan 30 2022

Mathematica

LinearRecurrence[{16,-69,54}, {1,16,187}, 41] (* G. C. Greubel, Jan 30 2022 *)

PARI

Vec(1/((1-x)*(1-6*x)*(1-9*x)) + O(x^40)) \\ Michel Marcus, Sep 04 2017

Sage

[(1 -16*6^(n+1) +15*9^(n+1))/40 for n in (0..40)] #  G. C. Greubel, Jan 30 2022

Formula

a(n) = (1 - 96*6^n + 135*9^n)/40. - Neven Juric, Oct 22 2009

a(0)=1, a(1)=16, a(n) = 15*a(n-1) - 54*a(n-2) + 1. - Vincenzo Librandi, Feb 10 2011

E.g.f.: (1/40)*(exp(x) - 96*exp(6*x) + 135*exp(9*x)). - G. C. Greubel, Jan 30 2022