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A180926
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Numbers a(n) such that 6*a(n) and 10*a(n) are both triangular numbers.
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1
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0, 1, 63, 3906, 242110, 15006915, 930186621, 57656563588, 3573776755836, 221516502298245, 13730449365735355, 851066344173293766, 52752382889378478138, 3269796672797292350791, 202674641330542747270905
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OFFSET
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1,3
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COMMENTS
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Subsequence of A154293. - Michel Marcus, Jun 25 2014
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (63,-63,1).
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FORMULA
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a(n) = (62*a(n-1)+1+((48*a(n-1)+1)*(80*a(n-1)+1))^(1/2))/2 with a(1)=0.
G.f.: -x^2 / ((x-1)*(x^2-62*x+1)). - Colin Barker, Jun 25 2014
a(n) = (-8+(4+sqrt(15))*(31+8*sqrt(15))^(-n)-(-4+sqrt(15))*(31+8*sqrt(15))^n)/480. - Colin Barker, Mar 03 2016
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MATHEMATICA
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a[1] = 0; a[n_] := a[n] = (62 a[n - 1] + 1 + Sqrt[(48 a[n - 1] + 1)*(80 a[n - 1] + 1)])/2; Array[a, 14] (* Robert G. Wilson v, Sep 27 2010 *)
Rest[CoefficientList[Series[-x^2/((x - 1) (x^2 - 62 x + 1)), {x, 0, 30}], x]] (* Vincenzo Librandi, Jun 26 2014 *)
LinearRecurrence[{63, -63, 1}, {0, 1, 63}, 20] (* Harvey P. Dale, Dec 25 2019 *)
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PROG
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(PARI) isok(n) = ispolygonal(6*n, 3) && ispolygonal(10*n, 3); \\ Michel Marcus, Jun 25 2014
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CROSSREFS
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Sequence in context: A051589 A203457 A258684 * A267963 A268028 A194484
Adjacent sequences: A180923 A180924 A180925 * A180927 A180928 A180929
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KEYWORD
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easy,nonn
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AUTHOR
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Vladimir Pletser, Sep 25 2010
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EXTENSIONS
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a(8) onwards from Robert G. Wilson v, Sep 27 2010
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STATUS
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approved
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