A053535 Expansion of 1/((1+3*x)*(1-9*x)).

1, 6, 63, 540, 4941, 44226, 398763, 3586680, 32286681, 290560446, 2615103063, 23535750420, 211822285221, 1906398972666, 17157595536963, 154418345483760, 1389765152400561, 12507886242464886, 112570976569604463

Offset

0,2

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Links

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

Index entries for linear recurrences with constant coefficients, signature (6,27).

Formula

a(n) = (3^n/4)*(3^(n+1) + (-1)^n).

a(n) = 6*a(n-1) + 27*a(n-2), with a(0)=1, a(1)=6.

E.g.f.: (3*exp(9*x) + exp(-3*x))/4. - G. C. Greubel, May 16 2019

Mathematica

LinearRecurrence[{6, 27}, {1, 6}, 20] (* G. C. Greubel, May 16 2019 *)

Prog

(PARI) my(x='x+O('x^20)); Vec(1/((1+3*x)*(1-9*x))) \\ G. C. Greubel, May 16 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 1/((1+3*x)*(1-9*x)) )); // G. C. Greubel, May 16 2019
(Sage) (1/((1+3*x)*(1-9*x))).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019
(GAP) a:=[1, 6];; for n in [3..30] do a[n]:=6*a[n-1]+27*a[n-2]; od; a; # G. C. Greubel, May 16 2019

Crossrefs

Cf. A015518.

Sequence in context: A123615 A245754 A267248 * A268220 A272495 A039937

Adjacent sequences: A053532 A053533 A053534 * A053536 A053537 A053538

Keyword

easy,nonn

Author

Barry E. Williams, Jan 15 2000

Status

approved