OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: Product_{i>0} (1+x^(2*i-1)-x^(4*i-2))/(1-x^(2*i)).
a(n) ~ sqrt(Pi^2/3 + 4*log(phi)^2) * exp(sqrt((Pi^2/3 + 4*log(phi)^2)*n)) / (4*Pi*n), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jan 03 2016
EXAMPLE
a(7) = 4 because we have 7, 322, 22111 and 1111111.
MAPLE
g:=product((1+x^(2*i-1)-x^(4*i-2))/(1-x^(2*i)), i=1..40): gser:=series(g, x=0, 60): seq(coeff(gser, x, n), n=0..55); # Emeric Deutsch, Aug 23 2007
# second Maple program:
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
add(`if`(irem(i+j, 2)=0, b(n-i*j, i-1), 0), j=1..n/i)
+b(n, i-1)))
end:
a:= n-> b(n$2):
seq(a(n), n=0..60); # Alois P. Heinz, May 31 2014
MATHEMATICA
nmax = 50; CoefficientList[Series[Product[(1 + x^(2*k-1) - x^(4*k-2))/(1-x^(2*k)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Jan 03 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Aug 16 2007
EXTENSIONS
More terms from Emeric Deutsch, Aug 23 2007
STATUS
approved