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Search: id:A004652
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| A004652 |
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Expansion of x*(1+x^2+x^4)/((1-x)*(1-x^2)*(1-x^3)). |
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+0
10
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| 0, 1, 1, 3, 4, 7, 9, 13, 16, 21, 25, 31, 36, 43, 49, 57, 64, 73, 81, 91, 100, 111, 121, 133, 144, 157, 169, 183, 196, 211, 225, 241, 256, 273, 289, 307, 324, 343, 361, 381, 400, 421, 441, 463, 484, 507, 529, 553, 576, 601, 625, 651, 676, 703, 729, 757, 784, 813
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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As a Molien series this arises as (1+x^12)/((1-x^4)*(1-x^8)^2).
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LINKS
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G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
A. R. Calderbank and N. J. A. Sloane, Double circulant codes over Z_4, J. Algeb. Combin., 6 (1997) 119-131 (Abstract, pdf, ps).
Index entries for Molien series
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FORMULA
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ceiling(n^2/4).
G.f.: x*(1-x+x^2)/((1-x)^2*(1-x^2)).
a(n) = a(n-1)+a(n-2)-a(n-3)+1. a(2*n) = n^2, a(2*n-1) = n^2-n+1 - Michael Somos, Apr 21, 2000.
Interleaves square numbers with centered polygonal numbers. a(2n)=A000290(n). a(2n+1)=A002061(n+1). - Paul Barry (pbarry(AT)wit.ie), Mar 13 2003
For n>1: a(n) is the digit reversal of n in base A008619(n), where a(n) is written in base 10. - Naohiro Nomoto (pcmusume(AT)m11.alpha-net.ne.jp), Mar 15 2004
a(n)=a(n-2)+n-1 - Paul Barry (pbarry(AT)wit.ie), Jul 14 2004
Euler transform of length 6 sequence [ 1, 2, 1, 0, 0, -1]. - Michael Somos Apr 03 2007
Starting (1, 3, 4, 7, 9, 13,...), = row sums of triangle A135840. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 01 2007
a(n)=(3/8)*(-1)^(n+1)+(5/8)-(3/4)*(n+1)+(1/4)*(n+2)*(n+1) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 27 2008]
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MAPLE
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with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r), right=Set(U, card<r), U=Sequence(Z, card>=2)}, unlabeled]: subs(r=1, stack): seq(count(subs(r=2, ZL), size=m), m=3..57) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 09 2007
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PROGRAM
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(PARI) a(n)=ceil(n^2/4)
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CROSSREFS
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First differences give A028242. Cf. A035104, A035106.
A002061(n)=a(2*n-1). A035104(n)=a(n+7)-12. A035106(n)=a(n+3)-1.
Cf. A135840.
Sequence in context: A073273 A072441 A152032 this_sequence A061568 A146994 A103054
Adjacent sequences: A004649 A004650 A004651 this_sequence A004653 A004654 A004655
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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