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A259404 Pentagonal numbers (A000326) that are the sum of twelve consecutive pentagonal numbers. 5
417912, 9706632, 3050311681782, 70865417283102, 22269721626195937752, 517374380230514907672, 162586828187971503638961822, 3777247909935632832763236342, 1187014240408376459988712771009992, 27576939095353370682323270116205112 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Sequence in context: A236909 A104920 A151838 * A116936 A255081 A206315
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 26 2015
STATUS
approved

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Last modified July 21 02:16 EDT 2024. Contains 374462 sequences. (Running on oeis4.)