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A245679
a(n) = pg(n, 3) + pg(n, 4) + ... + pg(n, n) where pg(n, m) is the m-th n-th-order polygonal number.
3
0, 0, 0, 6, 25, 69, 154, 300, 531, 875, 1364, 2034, 2925, 4081, 5550, 7384, 9639, 12375, 15656, 19550, 24129, 29469, 35650, 42756, 50875, 60099, 70524, 82250, 95381, 110025, 126294, 144304, 164175, 186031, 210000, 236214, 264809, 295925, 329706, 366300
OFFSET
0,4
COMMENTS
This is also [0, 0, 0] together with the partial sums of the terms of A005900 that are greater than 1. - J. M. Bergot, Jun 02 2022
FORMULA
a(n) = (-6 - n + 2*n^2 - 2*n^3 + n^4)/6 for n>1.
G.f.: x^3*(x-3)*(x^2-x+2) / (x-1)^5.
EXAMPLE
a(5) = pg(5, 3) + pg(5, 4) + pg(5, 5) = 12 + 22 + 35 = 69.
MATHEMATICA
CoefficientList[Series[x^3 (x - 3) (x^2 - x + 2)/(x - 1)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 01 2014 *)
PROG
(PARI) pg(n, m) = (m^2*(n-2)-m*(n-4))/2
vector(50, n, sum(m=3, n-1, pg(n-1, m)))
CROSSREFS
Sequence in context: A096958 A166814 A241170 * A354392 A211911 A339194
KEYWORD
nonn,easy
AUTHOR
Colin Barker, Jul 29 2014
STATUS
approved