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

0,2

Comments

Antidiagonal sums of the convolution array A213825.

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).

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

Example

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]

Mathematica

(See A213825.)

Prog

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

Crossrefs

Cf. A213825.

Sequence in context: A212257 A034520 A111128 * A129556 A077209 A369754

Adjacent sequences: A213824 A213825 A213826 * A213828 A213829 A213830

Keyword

nonn,easy

Author

Clark Kimberling, Jul 04 2012

Extensions

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

Status

approved