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A254964
Indices of heptagonal numbers (A000566) that are also centered hexagonal numbers (A003215).
3
1, 2, 14, 37, 301, 806, 6602, 17689, 144937, 388346, 3182006, 8525917, 69859189, 187181822, 1533720146, 4109474161, 33671984017, 90221249714, 739249928222, 1980758019541, 16229826436861, 43486455180182, 356316931682714, 954721255944457, 7822742670582841
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 5*x^2 - 6*y^2 - 3*x + 6*y - 2 = 0, the corresponding values of y being A254965.
FORMULA
a(n) = a(n-1)+22*a(n-2)-22*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^2-3*x+1)*(x^2+4*x+1) / ((x-1)*(x^4-22*x^2+1)).
EXAMPLE
14 is in the sequence because the 14th heptagonal number is 469, which is also the 13th centered hexagonal number.
MATHEMATICA
LinearRecurrence[{1, 22, -22, -1, 1}, {1, 2, 14, 37, 301}, 30] (* Harvey P. Dale, Apr 13 2018 *)
PROG
(PARI) Vec(-x*(x^2-3*x+1)*(x^2+4*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