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A254675
Indices of centered triangular numbers (A005448) which are also heptagonal numbers (A000566).
3
1, 13, 44, 776, 2697, 48069, 167140, 2979472, 10359953, 184679165, 642149916, 11447128728, 39802934809, 709537301941, 2467139808212, 43979865591584, 152922865174305, 2726042129376237, 9478750500998668, 168970632155735080, 587529608196743081
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 5*x^2 - 3*y^2 - 3*x + 3*y - 2 = 0, the corresponding values of x being A254674.
FORMULA
a(n) = a(n-1)+62*a(n-2)-62*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(12*x^3+31*x^2-12*x-1) / ((x-1)*(x^2-8*x+1)*(x^2+8*x+1)).
EXAMPLE
13 is in the sequence because the 13th centered triangular number is 235, which is also the 10th heptagonal number.
PROG
(PARI) Vec(x*(12*x^3+31*x^2-12*x-1)/((x-1)*(x^2-8*x+1)*(x^2+8*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 05 2015
STATUS
approved