Search: id:A028310
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%I A028310
%S A028310 1,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,
%T A028310 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,
%U A028310 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71
%N A028310 Expansion of (1-x+x^2)/(1-x)^2.
%C A028310 Molien series for ring of Hamming weight enumerators of self-dual codes 
               (with respect to Euclidean inner product) of length n over GF(4).
%C A028310 Engel expansion of e (see A006784 for definition) [when offset by 1] 
               - Henry Bottomley (se16(AT)btinternet.com), Dec 18 2000
%H A028310 G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://www.research.att.com/
               ~njas/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, 
               Springer, Berlin, 2006.
%H A028310 E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook 
               of Coding Theory, Elsevier, 1998 (<a href="http://www.research.att.com/
               ~njas/doc/self.txt">Abstract</a>, <a href="http://www.research.att.com/
               ~njas/doc/self.pdf">pdf</a>, <a href="http://www.research.att.com/
               ~njas/doc/self.ps">ps</a>).
%H A028310 <a href="Sindx_Mo.html#Molien">Index entries for Molien series</a>
%H A028310 <a href="Sindx_El.html#Engel">Index entries for sequences related to 
               Engel expansions</a>
%F A028310 Binomial transform is A005183. - Paul Barry (pbarry(AT)wit.ie), Jul 21 
               2003
%F A028310 G.f.: (1-x+x^2)/(1-x)^2 = (1-x^6)/((1-x)(1-x^2)(1-x^3)) = (1+x^3)/((1-x)*(1-x^2)).
%F A028310 Euler transform of length 6 sequence [ 1, 1, 1, 0, 0, -1]. - Michael 
               Somos Jul 30 2006
%F A028310 a(n) = Sum_{k, 0<=k<=n} A123110(n,k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Oct 06 2009]
%o A028310 (PARI) a(n)=(n==0)+max(n,0)
%Y A028310 Apart from the extra initial 1, same as A000027.
%Y A028310 Sequence in context: A069782 A088480 A061019 this_sequence A097045 A118759 
               A118760
%Y A028310 Adjacent sequences: A028307 A028308 A028309 this_sequence A028311 A028312 
               A028313
%K A028310 nonn,easy,mult
%O A028310 0,3
%A A028310 N. J. A. Sloane (njas(AT)research.att.com).

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