A097115 Expansion of (1 + 11*x - 90*x^2 - 1100*x^3)/(1 - 201*x^2 + 10100*x^4).

1, 11, 111, 1111, 12211, 112211, 1333311, 11333311, 144664411, 1144664411, 15611105511, 115611105511, 1676721656611, 11676721656611, 179348887317711, 1179348887317711, 19114237619088811, 119114237619088811, 2030537999527969911, 12030537999527969911, 215084337952324961011

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for linear recurrences with constant coefficients, signature (0,201,0,-10100).

Formula

G.f.: 11*(1+x)/(1-101*x^2) - 10/(1-100*x^2);

a(n) = 201*a(n-2) - 10100*a(n-4);

a(n) = (11/2 + 11*sqrt(101)/202)*sqrt(101)^n + (11/2 - 11*sqrt(101)/202)*(-sqrt(101))^n - 10^(n+1)*(1+(-1)^n)/2;

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

Mathematica

LinearRecurrence[ {0, 201, 0, -10100}, {1, 11, 111, 1111}, 18] (* Georg Fischer, Nov 07 2019 *)

Prog

(PARI) Vec((1+11*x-90*x^2-1100*x^3)/(1-201*x^2+10100*x^4) + O(x^25)) \\ Jinyuan Wang, Feb 28 2020

Crossrefs

Sequence in context: A294348 A078998 A078191 * A346789 A134732 A166747

Adjacent sequences: A097112 A097113 A097114 * A097116 A097117 A097118

Keyword

nonn,easy

Author

Paul Barry, Jul 25 2004

Extensions

More terms from Jinyuan Wang, Feb 28 2020

Status

approved