|
| |
| |
|
|
|
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
(list; graph; refs; listen; history; internal format)
|
|
|
|
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. [From 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
|
|
|
FORMULA
| a(n) = Sum[i=0, n][(i(i-2)^2+i^2)/2].
a(n)=A004255(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 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 [From Johannes W. Meijer, Apr 29 2011]
|
|
|
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}]] (* From 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
|
|
|
CROSSREFS
| Cf. A060354, A000332.
Sequence in context: A112522 A005262 A004255 * A065971 A145127 A096260
Adjacent sequences: A101354 A101355 A101356 * A101358 A101359 A101360
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 25 2004
|
|
|
EXTENSIONS
| More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 12 2006
Edited by Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Aug 01 2007
|
| |
|
|
