cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A097992 G.f.: 1/((1-x)*(1-x^6)) = 1/ ( (1+x)*(x^2-x+1)*(1+x+x^2)*(x-1)^2 ).

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%I A097992 #25 Dec 27 2023 08:54:54
%S A097992 1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,
%T A097992 6,6,7,7,7,7,7,7,8,8,8,8,8,8,9,9,9,9,9,9,10,10,10,10,10,10,11,11,11,
%U A097992 11,11,11,12,12,12,12,12,12,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15
%N A097992 G.f.: 1/((1-x)*(1-x^6)) = 1/ ( (1+x)*(x^2-x+1)*(1+x+x^2)*(x-1)^2 ).
%H A097992 G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%H A097992 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H A097992 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A097992 Molien series is 1/((1-x^2)*(1-x^12)).
%F A097992 a(n)=1+floor(n/6)
%F A097992 a(n)=1+(6*n-15+3*(-1)^n+12*sin[(2*n+1)*Pi/6]+4*sqrt(3)*sin[(2*n+1)*Pi/3])/36
%t A097992 CoefficientList[Series[1/((1-x)(1-x^6)),{x,0,90}],x] (* or *) LinearRecurrence[{1,0,0,0,0,1,-1},{1,1,1,1,1,1,2},90] (* _Harvey P. Dale_, Oct 29 2023 *)
%Y A097992 Apart from initial terms, same as A054895.
%K A097992 nonn
%O A097992 0,7
%A A097992 _N. J. A. Sloane_, Sep 07 2004