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

Author

Colin Barker, Jun 26 2015

Keywords

• nonn
• easy

Examples

			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).
		

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).

Crossrefs

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

Programs

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 *)

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))

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))