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A280072
Indices of centered 11-gonal numbers (A060544) that are also 11-gonal numbers (A051682).
2
1, 11, 210, 4180, 83381, 1663431, 33185230, 662041160, 13207637961, 263490718051, 5256606723050, 104868643742940, 2092116268135741, 41737456718971871, 832657018111301670, 16611402905507061520, 331395401092029928721, 6611296618935091512891
OFFSET
1,2
COMMENTS
Also positive integers y in the solutions to 9*x^2 - 11*y^2 - 7*x + 11*y - 2 = 0, the corresponding values of x being A280071.
FORMULA
a(n) = (6 - (3+sqrt(11))*(10+3*sqrt(11))^(-n) + (-3+sqrt(11))*(10+3*sqrt(11))^n)/12.
a(n) = 21*a(n-1) - 21*a(n-2) + a(n-3) for n>3.
G.f.: x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)).
EXAMPLE
11 is in the sequence because the 11th centered 11-gonal number is 606, which is also the 12th 11-gonal number.
MATHEMATICA
LinearRecurrence[{21, -21, 1}, {1, 11, 210}, 20] (* Harvey P. Dale, Aug 19 2020 *)
PROG
(PARI) Vec(x*(1 - 10*x) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30)) \\ Colin Barker, Dec 25 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Dec 25 2016
STATUS
approved