|
Search: id:A084634
|
|
|
| A084634 |
|
Binomial transform of 1,1,1,2,2,2,2,..... |
|
+0
5
|
|
| 1, 2, 4, 9, 21, 48, 106, 227, 475, 978, 1992, 4029, 8113, 16292, 32662, 65415, 130935, 261990, 524116, 1048385, 2096941, 4194072, 8388354, 16776939, 33554131, 67108538, 134217376, 268435077, 536870505, 1073741388, 2147483182
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Partial sums of A000325.
|
|
FORMULA
|
a(n)=2^(n+1)-(n^2+n+2)/2; a(n)=1+n+n(n-1)/2+2*sum{k=3..n, C(n, k)}.
O.g.f.: (1-3x+3x^2)/[(1-2x)(1-x)^3]. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2008
a(n)=5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2008
|
|
PROGRAM
|
(Other) sage: [gaussian_binomial(n, 1, 2)-binomial(n, 2) for n in xrange(1, 32)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
|
|
CROSSREFS
|
Sequence in context: A091619 A061439 A027711 this_sequence A137256 A051164 A101891
Adjacent sequences: A084631 A084632 A084633 this_sequence A084635 A084636 A084637
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Jun 06 2003
|
|
|
Search completed in 0.002 seconds
|
