A101357 Partial sums of A060354.

0, 1, 3, 9, 25, 60, 126, 238, 414, 675, 1045, 1551, 2223, 3094, 4200, 5580, 7276, 9333, 11799, 14725, 18165, 22176, 26818, 32154, 38250, 45175, 53001, 61803, 71659, 82650, 94860, 108376, 123288, 139689, 157675, 177345, 198801, 222148, 247494

Offset

0,3

Comments

The Ca4 triangle sums of A139600 are given by the terms of this sequence. For the definitions of the Ca4 and other triangle sums see A180662. - Johannes W. Meijer, Apr 29 2011

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Polygonal number

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

Formula

a(n) = Sum_{i=0..n} (i(i-2)^2 + i^2)/2.

a(n) = A004255(n), n > 0. - R. J. Mathar, Sep 02 2008

a(n) = binomial(n+3,4) - 2*binomial(n+2,4) + 4*binomial(n+1,4).

a(n) = (n^4 - 2*n^3 + 3*n^2 + 6*n)/8. - Johannes W. Meijer, Apr 29 2011

G.f.: -x*(4*x^2 - 2*x + 1) / (x-1)^5. - Colin Barker, Apr 29 2013

Mathematica

Table[Sum[(i*(i - 2)^2 + i^2)/2, {i, 0, n}], {n, 0, 38}]
Accumulate[Table[(n (n-2)^2+n^2)/2, {n, 0, 50}]] (* Harvey P. Dale, Aug 05 2011 *)

Prog

(Magma) [(n^4-2*n^3+3*n^2+6*n)/8: n in [0..40]]; // Vincenzo Librandi, Aug 06 2011
(PARI) a(n)=(n^4-2*n^3+3*n^2+6*n)/8 \\ Charles R Greathouse IV, Oct 16 2015

Crossrefs

Cf. A060354, A000332.

Sequence in context: A005209 A112522 A005262 * A004255 A065971 A145127

Adjacent sequences: A101354 A101355 A101356 * A101358 A101359 A101360

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 25 2004

Extensions

More terms from Joshua Zucker, May 12 2006

Edited by Stefan Steinerberger, Aug 01 2007

Status

approved