A259404 Pentagonal numbers (A000326) that are the sum of twelve consecutive pentagonal numbers.

417912, 9706632, 3050311681782, 70865417283102, 22269721626195937752, 517374380230514907672, 162586828187971503638961822, 3777247909935632832763236342, 1187014240408376459988712771009992, 27576939095353370682323270116205112

Offset

1,1

Links

Colin Barker, Table of n, a(n) for n = 1..290

Index entries for linear recurrences with constant coefficients, signature (1,7300802,-7300802,-1,1).

Formula

G.f.: -6*x*(377*x^4+7980*x^3-131798379*x^2+1548120*x+69652) / ((x-1)*(x^2-2702*x+1)*(x^2+2702*x+1))

Example

417912 is in the sequence because P(528) = 417912 = 32340 + 32782 + 33227 + 33675 + 34126 + 34580 + 35037 + 35497 + 35960 + 36426 + 36895 + 37367 = P(147)+ ... +P(158).

Mathematica

Select[Total/@Partition[PolygonalNumber[5, Range[5*10^6]], 12, 1], IntegerQ[ (1+Sqrt[ 1+24#])/6]&] (* The program generates the first four terms of the sequence. To generate more, increase the Range constant but the program will take a long time to run. *) (* Harvey P. Dale, Dec 17 2020 *)

Prog

(PARI) Vec(-6*x*(377*x^4+7980*x^3-131798379*x^2+1548120*x+69652) / ((x-1)*(x^2-2702*x+1)*(x^2+2702*x+1)) + O(x^20))

Crossrefs

Cf. A000326, A133301, A257714, A257715, A259402, A259403.

Sequence in context: A236909 A104920 A151838 * A116936 A255081 A206315

Adjacent sequences: A259401 A259402 A259403 * A259405 A259406 A259407

Keyword

nonn,easy

Author

Colin Barker, Jun 26 2015

Status

approved