0,4

a(n) ~ sqrt(6/pi)*n^(-3/2)*2^n for n = 0 or 3 (mod 4) as n approaches infinity (see H.-K. Hwang's review MR 2003j:05005 of the JIS paper)

Suggested by J. H. Conway (conway(AT)math.princeton.edu), Aug 27, 2001.

N. J. A. Sloane, Table of n, a(n) for n=0..400

S. R. Finch, Signum equations and extremal coefficients.

Dorin Andrica and Ioan Tomescu, On an Integer Sequence Related to a Product..., Journal of Integer Sequences, Vol. 5 (2002), Article 02.2.4

a(n) = 0 unless n == 0 or 3 (mod 4).

a(n) = constant term in expansion of Prod_{ k = 1..n } (x^k + 1/x^k). - N. J. A. Sloane (njas(AT)research.att.com), Jul 07 2008

If n = 0 or 3 (mod 4) then a(n) = coefficient of x^(n(n+1)/4) in Product_{k=1..n} (1+x^k). - D. Andrica and I. Tomescu.

M:=400; t1:=1; lprint(0, 1); for n from 1 to M do t1:=expand(t1*(x^n+1/x^n)); lprint(n, coeff(t1, x, 0)); od: - N. J. A. Sloane (njas(AT)research.att.com), Jul 07 2008

f[n_, s_] := f[n, s]=Which[n==0, If[s==0, 1, 0], Abs[s]>(n*(n+1))/2, 0, True, f[ n-1, s-n]+f[n-1, s+n]]; a[n_] := f[n, 0]

Cf. A025591, A063866, A063867, A000980, A141000. "Decimations": A060468, A123117 = 2*A104456.

Contribution from Pietro Majer (majer(AT)dm.unipi.it), Mar 15 2009: (Start)

Analogous sequences for sums of squares and cubes are A158092, A158118,

see also A019568. (End)

Sequence in context: A089262 A069971 A167291 this_sequence A037224 A122670 A087637

Adjacent sequences: A063862 A063863 A063864 this_sequence A063866 A063867 A063868

nonn,easy,nice

N. J. A. Sloane (njas(AT)research.att.com), Aug 27 2001

More terms from Dean Hickerson, Aug 28, 2001

Corrected and edited by S. R. Finch (Steven.Finch(AT)inria.fr), Feb 01 2009