A181719 a(n) = A133473(n+1)^2.
25, 1225, 112225, 11122225, 1111222225, 111112222225, 11111122222225, 1111111222222225, 111111112222222225, 11111111122222222225, 1111111111222222222225, 111111111112222222222225, 11111111111122222222222225, 1111111111111222222222222225, 111111111111112222222222222225
Offset: 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).
Programs
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Magma
[(100^n+10*10^n+25)/9: n in [1..20]]; // Vincenzo Librandi, Jun 02 2011
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Mathematica
(5+10^Range[30])^2/9 (* G. C. Greubel, Mar 25 2024 *) LinearRecurrence[{111,-1110,1000},{25,1225,112225},20] (* Harvey P. Dale, Feb 22 2025 *)
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PARI
a(n)=(100^n+10*10^n+25)/9 \\ Charles R Greathouse IV, Jun 01 2011
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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
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SageMath
[(5+10^n)^2//9 for n in range(1,31)] # G. C. Greubel, Mar 25 2024
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
Extensions
Formulas edited by Eric M. Schmidt, Oct 29 2012