login
A254628
Triangular numbers (A000217) that are also centered pentagonal numbers (A005891).
4
1, 6, 276, 1891, 88831, 608856, 28603266, 196049701, 9210162781, 63127394826, 2965643812176, 20326825084231, 954928097357851, 6545174549727516, 307483881705415806, 2107525878187175881, 99008854981046531641, 678616787601720906126, 31880543820015277772556
OFFSET
1,2
COMMENTS
Also hexagonal numbers (A000384) that are also centered pentagonal numbers (A005891). - Colin Barker, Feb 11 2015
FORMULA
a(n) = a(n-1)+322*a(n-2)-322*a(n-3)-a(n-4)+a(n-5).
G.f.: -x*(x^4+5*x^3-52*x^2+5*x+1) / ((x-1)*(x^2-18*x+1)*(x^2+18*x+1)).
EXAMPLE
6 is in the sequence because it is the 3rd triangular number and the 2nd centered pentagonal number.
PROG
(PARI) Vec(-x*(x^4+5*x^3-52*x^2+5*x+1)/((x-1)*(x^2-18*x+1)*(x^2+18*x+1)) + O(x^100))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Feb 03 2015
STATUS
approved