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A254653
Indices of centered heptagonal numbers (A069099) which are also pentagonal numbers (A000326).
3
1, 3, 58, 276, 6325, 30303, 695638, 3333000, 76513801, 366599643, 8415822418, 40322627676, 925663952125, 4435122444663, 101814618911278, 487823146285200, 11198682416288401, 53656110968927283, 1231753251172812778, 5901684383435715876, 135481658946593117125
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 3*x^2 - 7*y^2 - x + 7*y - 2 = 0, the corresponding values of x being A254652.
FORMULA
a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(2*x^3+55*x^2-2*x-1) / ((x-1)*(x^4-110*x^2+1)).
EXAMPLE
3 is in the sequence because the 3rd centered heptagonal number is 22, which is also the 4th pentagonal number.
PROG
(PARI) Vec(x*(2*x^3+55*x^2-2*x-1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 04 2015
STATUS
approved