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A254965
Indices of centered hexagonal numbers (A003215) that are also heptagonal numbers (A000566).
3
1, 2, 13, 34, 275, 736, 6027, 16148, 132309, 354510, 2904761, 7783062, 63772423, 170872844, 1400088535, 3751419496, 30738175337, 82360356058, 674839768869, 1808176413770, 14815736739771, 39697520746872, 325271368506083, 871537280017404, 7141154370394045
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 5*x^2 - 6*y^2 - 3*x + 6*y - 2 = 0, the corresponding values of x being A254964.
FORMULA
a(n) = a(n-1)+22*a(n-2)-22*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(x^3+11*x^2-x-1) / ((x-1)*(x^4-22*x^2+1)).
EXAMPLE
13 is in the sequence because the 13th centered hexagonal number is 469, which is also the 14th heptagonal number.
PROG
(PARI) Vec(x*(x^3+11*x^2-x-1)/((x-1)*(x^4-22*x^2+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 11 2015
STATUS
approved