A253922 Indices of centered pentagonal numbers (A005891) which are also octagonal numbers (A000567).
1, 56, 297, 26752, 142913, 12894168, 68883529, 6214961984, 33201717825, 2995598781880, 16003159107881, 1443872397903936, 7713489488280577, 695943500190915032, 3717885930192129993, 335443323219623141248, 1792013304863118375809, 161682985848358163166264
Offset: 1
Examples
56 is in the sequence because the 56th centered pentagonal is 7701, which is also the number 51st octagonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..745
- Index entries for linear recurrences with constant coefficients, signature (1,482,-482,-1,1).
Programs
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Magma
I:=[1,56,297,26752,142913]; [n le 5 select I[n] else Self(n-1)+482*Self(n-2)-482*Self(n-3)-Self(n-4)+Self(n-5): n in [1..25]]; // Vincenzo Librandi, Jan 20 2015
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Mathematica
CoefficientList[Series[(55 x^3 + 241 x^2 - 55 x - 1)/((x - 1)(x^2 - 22 x + 1) (x^2 + 22 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2015 *) -
PARI
Vec(x*(55*x^3+241*x^2-55*x-1)/((x-1)*(x^2-22*x+1)*(x^2+22*x+1)) + O(x^100))
Formula
a(n) = a(n-1)+482*a(n-2)-482*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(55*x^3+241*x^2-55*x-1) / ((x-1)*(x^2-22*x+1)*(x^2+22*x+1)).
Comments