OFFSET
0,4
LINKS
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).
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
EXAMPLE
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
MATHEMATICA
a[ n_] := Ceiling[(n + 1)^2/12]; (* Michael Somos, Dec 16 2021 *)
PROG
(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 */
(PARI) {a(n) = (n^2 + 2*n)\12 + 1}; /* Michael Somos, Dec 16 2021 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved