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%I #45 Dec 17 2021 01:22:36
%S 1,1,1,2,3,3,5,6,7,9,11,12,15,17,19,22,25,27,31,34,37,41,45,48,53,57,
%T 61,66,71,75,81,86,91,97,103,108,115,121,127,134,141,147,155,162,169,
%U 177,185,192,201,209,217,226,235,243,253,262,271,281
%N G.f.: (1+x^6)/((1-x)*(1-x^3)*(1-x^4)).
%H 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 <a href="/index/Mo#Molien">Index entries for Molien series</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F a(n) = ceiling((n+1)^2/12).
%F From _R. J. Mathar_, Jan 22 2011: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).
%F G.f.: ( -1-x^4+x^2 ) / ( (1+x)*(1+x+x^2)*(x-1)^3 ). (End)
%F From _R. J. Mathar_, Jan 14 2021: (Start)
%F a(n) - a(n-1) = A008612(n).
%F Empirical: a(n) + a(n+1) = A266542(n).
%F 72*a(n) = 6*n^2 + 12*n + 47 + 9*(-1)^n + 16*A061347(n+1). (End)
%F a(n) = a(-2-n) for all n in Z. - _Michael Somos_, Dec 16 2021
%e G.f. = 1 + x + x^2 + 2*x^3 + 3*x^4 + 3*x^5 + 5*x^6 + 6*x^7 + ... - _Michael Somos_, Dec 16 2021
%t a[ n_] := Ceiling[(n + 1)^2/12]; (* _Michael Somos_, Dec 16 2021 *)
%o (Maxima) makelist(coeff(taylor((1+x^6)/((1-x)*(1-x^3)*(1-x^4)),x,0,n),x,n),n,0,57); /* _Bruno Berselli_, May 30 2011 */
%o (PARI) {a(n) = (n^2 + 2*n)\12 + 1}; /* _Michael Somos_, Dec 16 2021 */
%Y Cf. A008724, A001399.
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_
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