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A280071
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Indices of 11-gonal numbers (A051682) that are also centered 11-gonal numbers (A060544).
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2
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1, 12, 232, 4621, 92181, 1838992, 36687652, 731914041, 14601593161, 291299949172, 5811397390272, 115936647856261, 2312921559734941, 46142494546842552, 920536969377116092, 18364596892995479281, 366371400890532469521, 7309063420917653911132
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..750
Index entries for linear recurrences with constant coefficients, signature (21,-21,1).
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FORMULA
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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)).
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EXAMPLE
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12 is in the sequence because the 12th 11-gonal number is 606, which is also the 11th centered 11-gonal number.
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PROG
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(PARI) Vec(x*(1 - 9*x + x^2) / ((1 - x)*(1 - 20*x + x^2)) + O(x^30))
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CROSSREFS
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Cf. A051682, A060544, A131215, A280072
Sequence in context: A171093 A089343 A303487 * A279610 A222702 A352700
Adjacent sequences: A280068 A280069 A280070 * A280072 A280073 A280074
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Dec 25 2016
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STATUS
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approved
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