A254711 Pentagonal numbers (A000326) which are also centered square numbers (A001844).
1, 5, 145, 925, 28085, 179401, 5448301, 34802825, 1056942265, 6751568605, 205041351065, 1309769506501, 39776965164301, 254088532692545, 7716526200523285, 49291865572847185, 1496966305936352945, 9562367832599661301, 290403746825451948001
Offset: 1
Examples
145 is in the sequence because it is the 10th pentagonal number and the 9th centered square number.
Links
- Colin Barker, Table of n, a(n) for n = 1..875
- Index entries for linear recurrences with constant coefficients, signature (1,194,-194,-1,1).
Programs
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PARI
Vec(-x*(x^4+4*x^3-54*x^2+4*x+1)/((x-1)*(x^2-14*x+1)*(x^2+14*x+1)) + O(x^100))
Formula
a(n) = a(n-1)+194*a(n-2)-194*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+4*x^3-54*x^2+4*x+1) / ((x-1)*(x^2-14*x+1)*(x^2+14*x+1)).