OFFSET
0,9
COMMENTS
Note that this sequence contains four plateaus: [1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4], [13, 13, 13, 13], [35, 35]. For more information see A210843 and other sequences of this family. - Omar E. Pol, Jun 29 2012
FORMULA
G.f.: Product_{k>=1} 1/((1 - x^(9*k))*(1 - x^(9*k-1))*(1 - x^(9*k-8))). - Ilya Gutkovskiy, Aug 13 2017
a(n) ~ exp(Pi*sqrt(2*n)/3) / (8*sin(Pi/9)*n). - Vaclav Kotesovec, Aug 14 2017
MAPLE
A195160 := proc(n)
(18*n*(n+1)+5*(2*n+1)*(-1)^n-5)/16 ;
end proc:
A195841 := proc(n, k)
option remember;
local ks, a, j ;
if A195160(k) > n then
0 ;
elif n <= 5 then
return 1;
elif k = 1 then
a := 0 ;
for j from 1 do
if A195160(j) <= n-1 then
a := a+procname(n-1, j) ;
else
break;
end if;
end do;
return a;
else
ks := A195160(k) ;
(-1)^floor((k-1)/2)*procname(n-ks+1, 1) ;
end if;
end proc:
A195851 := proc(n)
A195841(n+1, 1) ;
end proc:
seq(A195851(n), n=0..60) ; # R. J. Mathar, Oct 08 2011
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 07 2011
STATUS
approved