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A248205
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Indices of centered octagonal numbers (A016754) that are also pentagonal numbers (A000326).
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3
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1, 50, 4851, 475300, 46574501, 4563825750, 447208348951, 43821854371400, 4294094520048201, 420777441110352250, 41231895134294472251, 4040304945719747928300, 395908652785401002501101, 38795007668023578497179550, 3801514842813525291721094751
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OFFSET
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1,2
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COMMENTS
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Positive integers y in the solutions to 3*x^2 - 8*y^2 - x + 8*y - 2 = 0, the corresponding values of x being A046172.
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LINKS
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FORMULA
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a(n) = 99*a(n-1) - 99*a(n-2) + a(n-3).
G.f.: x*(49*x-1) / ((x-1)*(x^2 - 98*x + 1)).
a(n) = (1/2+1/48*(49+20*sqrt(6))^(-n)*(-12-5*sqrt(6)+(-12+5*sqrt(6))*(49+20*sqrt(6))^(2*n))). - Colin Barker, Mar 03 2016
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EXAMPLE
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50 is in the sequence because the 50th centered octagonal number is 9801, which is also the 81st pentagonal number.
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MATHEMATICA
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LinearRecurrence[{99, -99, 1}, {1, 50, 4851}, 20] (* Vincenzo Librandi, Jun 13 2015 *)
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PROG
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(PARI) Vec(x*(49*x-1)/((x-1)*(x^2-98*x+1)) + O(x^100))
(Magma) I:=[1, 50, 4851]; [n le 3 select I[n] else 99*Self(n-1)-99*Self(n-2)+Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jun 13 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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