OFFSET
0,7
COMMENTS
Note that this sequence contains three plateaus: [1, 1, 1, 1, 1, 1], [4, 4, 4, 4], [13, 13]. For more information see A210843. See also other columns of A195825. - Omar E. Pol, Jun 29 2012
Number of partitions of n into parts congruent to 0, 1 or 6 (mod 7). - Ludovic Schwob, Aug 05 2021
LINKS
Ludovic Schwob, Table of n, a(n) for n = 0..10000
FORMULA
G.f.: Product_{k>=1} 1/((1 - x^(7*k))*(1 - x^(7*k-1))*(1 - x^(7*k-6))). - Ilya Gutkovskiy, Aug 13 2017
a(n) ~ exp(Pi*sqrt(2*n/7)) / (8*sin(Pi/7)*n). - Vaclav Kotesovec, Aug 14 2017
MAPLE
A118277 := proc(n)
7*n^2/8+7*n/8-3/16+3*(-1)^n*(1/16+n/8) ;
end proc:
A195839 := proc(n, k)
option remember;
local ks, a, j ;
if A118277(k) > n then
0 ;
elif n <= 5 then
return 1;
elif k = 1 then
a := 0 ;
for j from 1 do
if A118277(j) <= n-1 then
a := a+procname(n-1, j) ;
else
break;
end if;
end do;
return a;
else
ks := A118277(k) ;
(-1)^floor((k-1)/2)*procname(n-ks+1, 1) ;
end if;
end proc:
A195849 := proc(n)
A195839(n+1, 1) ;
end proc:
seq(A195849(n), n=0..60) ; # R. J. Mathar, Oct 08 2011
MATHEMATICA
m = 61;
Product[1/((1 - x^(7k))(1 - x^(7k - 1))(1 - x^(7k - 6))), {k, 1, m}] + O[x]^m // CoefficientList[#, x]& ( Jean-François Alcover, Apr 13 2020, after Ilya Gutkovskiy *)
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 07 2011
STATUS
approved