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A254782
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Indices of centered hexagonal numbers (A003215) which are also centered pentagonal numbers (A005891).
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3
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1, 11, 231, 5061, 111101, 2439151, 53550211, 1175665481, 25811090361, 566668322451, 12440892003551, 273132955755661, 5996484134620981, 131649518005905911, 2890292911995309051, 63454794545890893201, 1393115187097604341361, 30585079321601404616731
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OFFSET
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1,2
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COMMENTS
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Also positive integers y in the solutions to 5*x^2 - 6*y^2 - 5*x + 6*y = 0, the corresponding values of x being A133285.
The numbers (as opposed to the indices) are A133141.
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LINKS
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Colin Barker, Table of n, a(n) for n = 1..746
Index entries for linear recurrences with constant coefficients, signature (23,-23,1).
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FORMULA
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a(n) = 23*a(n-1)-23*a(n-2)+a(n-3).
G.f.: -x*(x^2-12*x+1) / ((x-1)*(x^2-22*x+1)).
a(n) = 1/2+1/24*(11+2*sqrt(30))^(-n)*(6+sqrt(30)-(-6+sqrt(30))*(11+2*sqrt(30))^(2*n)). - Colin Barker, Mar 03 2016
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EXAMPLE
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11 is in the sequence because the 11th centered hexagonal number is 331, which is also the 12th centered pentagonal number.
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PROG
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(PARI) Vec(-x*(x^2-12*x+1)/((x-1)*(x^2-22*x+1)) + O(x^100))
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CROSSREFS
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Cf. A003215, A005891, A133141, A133285.
Sequence in context: A077736 A068122 A015287 * A169960 A045757 A144773
Adjacent sequences: A254779 A254780 A254781 * A254783 A254784 A254785
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KEYWORD
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nonn,easy
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AUTHOR
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Colin Barker, Feb 07 2015
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STATUS
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approved
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