A361293 a(n) = 20 * a(n-1) - 90 * a(n-2) for n>1, with a(0)=0, a(1)=1.

0, 1, 20, 310, 4400, 60100, 806000, 10711000, 141680000, 1869610000, 24641000000, 324555100000, 4273412000000, 56258281000000, 740558540000000, 9747925510000000, 128308241600000000, 1688851536100000000, 22229288978000000000, 292589141311000000000

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Index entries for linear recurrences with constant coefficients, signature (20,-90).

Formula

a(n) = ( (10 + sqrt(10))^n - (10 - sqrt(10))^n )/(2 * sqrt(10)).

a(n) = Sum_{k=0..floor((n-1)/2)} 10^(n-1-k) * binomial(n,2*k+1).

G.f.: x/(1 - 20 * x + 90 * x^2).

E.g.f.: exp(10 * x) * sinh(sqrt(10) * x) / sqrt(10).

Mathematica

LinearRecurrence[{20, -90}, {0, 1}, 20] (* Harvey P. Dale, Dec 16 2023 *)

Prog

(PARI) a(n) = polcoef(lift(Mod('x, ('x-10)^2-10)^n), 1);
(PARI) my(N=20, x='x+O('x^N)); concat (0,  Vec(x/(1-20*x+90*x^2)))
(PARI) my(N=20, x='x+O('x^N)); concat (0, apply(round, Vec(serlaplace(exp(10*x)*sinh(sqrt(10)*x)/sqrt(10)))))

Crossrefs

Column k=10 of A361290.

Cf. A289414.

Sequence in context: A016188 A006300 A282372 * A240799 A281931 A034094

Adjacent sequences: A361290 A361291 A361292 * A361294 A361295 A361296

Keyword

nonn,easy

Author

Seiichi Manyama, Mar 12 2023

Status

approved