A213827 a(n) = n^2*(n+1)*(3*n+1)/4.

0, 2, 21, 90, 260, 600, 1197, 2156, 3600, 5670, 8525, 12342, 17316, 23660, 31605, 41400, 53312, 67626, 84645, 104690, 128100, 155232, 186461, 222180, 262800, 308750, 360477, 418446, 483140, 555060, 634725, 722672, 819456, 925650, 1041845, 1168650, 1306692

Offset: 0

Author

Clark Kimberling, Jul 04 2012

Keywords

• nonn
• easy

Comments

Antidiagonal sums of the convolution array A213825.

Examples

			a(7) = 1*(7^2+1) + 2*(7^2+2^2) + 3*(7^2+3^2) + 4*(7^2+4^2) + 5*(7^2+5^2) + 6*(7^2+6^2) + 7*(7^2+7^2) = 2156. [_Bruno Berselli_, Aug 25 2014]
		

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A213825.

Programs

Magma

[(n+1)*(3*n+1)*n^2/4: n in [1..40]]; // Bruno Berselli, Aug 25 2014

Mathematica

(See A213825.)

Sage

[(n+1)*(3*n+1)*n^2/4 for n in (1..40)] # Bruno Berselli, Aug 25 2014

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

G.f.: x*(2 + 11*x + 5*x^2) / (1-x)^5.

a(n) = Sum_{i=1..n} i*(n^2+i^2). - Bruno Berselli, Aug 25 2014

a(n) = (A367177(n) - 3*(n+1))/3. - Scott R. Shannon and N. J. A. Sloane, Nov 09 2023

Extensions

Edited by N. J. A. Sloane, May 14 2020 (changed offset, changed to simpler definition from Bruno Berselli).