A036410 G.f.: (1+x^6)/((1-x)*(1-x^3)*(1-x^4)).
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, 61, 66, 71, 75, 81, 86, 91, 97, 103, 108, 115, 121, 127, 134, 141, 147, 155, 162, 169, 177, 185, 192, 201, 209, 217, 226, 235, 243, 253, 262, 271, 281
Offset: 0
Examples
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
Links
- G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
- Index entries for Molien series
- Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).
Programs
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Mathematica
a[ n_] := Ceiling[(n + 1)^2/12]; (* Michael Somos, Dec 16 2021 *)
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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 */
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PARI
{a(n) = (n^2 + 2*n)\12 + 1}; /* Michael Somos, Dec 16 2021 */
Formula
a(n) = ceiling((n+1)^2/12).
From R. J. Mathar, Jan 22 2011: (Start)
a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6).
G.f.: ( -1-x^4+x^2 ) / ( (1+x)*(1+x+x^2)*(x-1)^3 ). (End)
From R. J. Mathar, Jan 14 2021: (Start)
a(n) - a(n-1) = A008612(n).
Empirical: a(n) + a(n+1) = A266542(n).
72*a(n) = 6*n^2 + 12*n + 47 + 9*(-1)^n + 16*A061347(n+1). (End)
a(n) = a(-2-n) for all n in Z. - Michael Somos, Dec 16 2021