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A280071
Indices of 11-gonal numbers (A051682) that are also centered 11-gonal numbers (A060544).
2
1, 12, 232, 4621, 92181, 1838992, 36687652, 731914041, 14601593161, 291299949172, 5811397390272, 115936647856261, 2312921559734941, 46142494546842552, 920536969377116092, 18364596892995479281, 366371400890532469521, 7309063420917653911132
OFFSET
1,2
COMMENTS
Also positive integers x in the solutions to 9*x^2 - 11*y^2 - 7*x + 11*y - 2 = 0, the corresponding values of y being A280072.
FORMULA
a(n) = (14 + (11-3*sqrt(11))*(10+3*sqrt(11))^n + (10+3*sqrt(11))^(-n)*(11+3*sqrt(11)))/36.
a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.
G.f.: x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)).
EXAMPLE
12 is in the sequence because the 12th 11-gonal number is 606, which is also the 11th centered 11-gonal number.
PROG
(PARI) Vec(x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 25 2016
STATUS
approved