A181719 a(n) = A133473(n+1)^2.

25, 1225, 112225, 11122225, 1111222225, 111112222225, 11111122222225, 1111111222222225, 111111112222222225, 11111111122222222225, 1111111111222222222225, 111111111112222222222225, 11111111111122222222222225, 1111111111111222222222222225, 111111111111112222222222222225

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

a(n) = 100 * A181718(n-1) + 25.

a(n) = 25 * A109344(n-1), for n > 1.

From Colin Barker, Aug 21 2019: (Start)

G.f.: x*(1 - 62*x + 160*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)).

a(n) = (5 + 10^n)^2 / 9.

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n>3. (End)

E.g.f.: (1/9)*exp(x)*(25 + 10*exp(9*x) + exp(99*x)). - Stefano Spezia, Aug 21 2019 after Colin Barker

Mathematica

(5+10^Range[30])^2/9 (* G. C. Greubel, Mar 25 2024 *)

Prog

(PARI) a(n)=(100^n+10*10^n+25)/9 \\ Charles R Greathouse IV, Jun 01 2011
(PARI) Vec(5*x*(1 - 62*x + 160*x^2) / ((1 - x)*(1 - 10*x)*(1 - 100*x)) + O(x^17)) \\ Colin Barker, Aug 21 2019
(Magma) [(100^n+10*10^n+25)/9: n in [1..20]]; // Vincenzo Librandi, Jun 02 2011
(SageMath) [(5+10^n)^2//9 for n in range(1, 31)] # G. C. Greubel, Mar 25 2024

Crossrefs

Cf. A109344, A133473, A181718.

Sequence in context: A012809 A014769 A012851 * A096330 A174751 A042203

Adjacent sequences: A181716 A181717 A181718 * A181720 A181721 A181722

Keyword

nonn,easy

Author

Paul Curtz, Nov 17 2010

Extensions

Formulas edited by Eric M. Schmidt, Oct 29 2012

Status

approved