A212335 Expansion of 1/(1-22*x+22*x^2-x^3).

1, 22, 462, 9681, 202840, 4249960, 89046321, 1865722782, 39091132102, 819048051361, 17160917946480, 359560228824720, 7533603887372641, 157846121406000742, 3307234945638642942, 69294087737005501041, 1451868607531476878920

Offset: 0

Author

Bruno Berselli, Jun 12 2012

Keywords

• nonn
• easy

Comments

Partial sums of A092499 (after 0).

Links

• Bruno Berselli, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (22,-22,1).

Crossrefs

Cf. A212336 for more sequences with g.f. of the type 1/(1-k*x+k*x^2-x^3).

Programs

Magma

m:=17; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-22*x+22*x^2-x^3)));

Maple

a:= n-> (<<0|1|0>, <0|0|1>, <1|-22|22>>^n. <<1, 22, 462>>)[1, 1]:
seq(a(n), n=0..20);  # Alois P. Heinz, Jun 15 2012

Mathematica

CoefficientList[Series[1/(1 - 22 x + 22 x^2 - x^3), {x, 0, 16}], x]
LinearRecurrence[{22,-22,1},{1,22,462},20] (* Harvey P. Dale, Nov 04 2017 *)

Maxima

makelist(coeff(taylor(1/(1-22*x+22*x^2-x^3), x, 0, n), x, n), n, 0, 16);

PARI

Vec(1/(1-22*x+22*x^2-x^3)+O(x^17))

Formula

G.f.: 1/((1-x)*(1-21*x+x^2)).

a(n) = (((230-11*sqrt(437))*(21-sqrt(437))^n+(230+11*sqrt(437))*(21+sqrt(437))^n)/2^n-23)/437.

a(n) = a(-n-3) = 23*a(n-1)-23*a(n-2)+a(n-3).

a(n)*a(n+2) = a(n+1)*(a(n+1)-1).