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.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Wikipedia, Polygonal number

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

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

Cf. A005900, A241452.

Sequence in context: A096958 A166814 A241170 * A354392 A211911 A339194

Adjacent sequences: A245676 A245677 A245678 * A245680 A245681 A245682

Keyword

nonn,easy

Author

Colin Barker, Jul 29 2014

Status

approved