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A254137
Indices of centered hexagonal numbers (A003215) which are also pentagonal numbers (A000326).
3
1, 52, 629, 59432, 725289, 68583900, 836982301, 79145760592, 965876849489, 91334139138692, 1114621047327429, 105399517420289400, 1286271722739003001, 121630951768874828332, 1484356453419762135149, 140362012941764131605152, 1712946060974682764958369
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 3*x^2 - 6*y^2 - x + 6*y - 2 = 0, the corresponding values of x being A254136.
FORMULA
a(n) = a(n-1)+1154*a(n-2)-1154*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(51*x^3+577*x^2-51*x-1) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).
EXAMPLE
52 is in the sequence because the 52nd centered hexagonal number is 7957, which is also the 73rd pentagonal number.
PROG
(PARI) Vec(x*(51*x^3+577*x^2-51*x-1)/((x-1)*(x^2-34*x+1)*(x^2+34*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jan 26 2015
STATUS
approved