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
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jun 26 2015
STATUS
approved