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A254711
Pentagonal numbers (A000326) which are also centered square numbers (A001844).
3
1, 5, 145, 925, 28085, 179401, 5448301, 34802825, 1056942265, 6751568605, 205041351065, 1309769506501, 39776965164301, 254088532692545, 7716526200523285, 49291865572847185, 1496966305936352945, 9562367832599661301, 290403746825451948001
OFFSET
1,2
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)).
EXAMPLE
145 is in the sequence because it is the 10th pentagonal number and the 9th centered square number.
PROG
(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))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 06 2015
STATUS
approved