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A195851
Column 7 of array A195825. Also column 1 of triangle A195841. Also 1 together with the row sums of triangle A195841.
14
1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 4, 4, 5, 7, 10, 12, 13, 13, 13, 13, 14, 16, 21, 27, 32, 34, 35, 35, 36, 38, 44, 54, 67, 77, 83, 85, 87, 89, 95, 107, 128, 152, 173, 185, 192, 196, 203, 216, 242, 281, 328, 367, 394, 409, 421, 436, 465
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
(GW-BASIC)' A program with two A-numbers:
10 Dim A195160(100), A057077(100), a(100): a(0)=1
20 For n = 1 to 61: For j = 1 to n
30 If A195160(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A195160(j))
40 Next j: Print a(n-1); : Next n
50 'Omar E. Pol, Jun 10 2012
KEYWORD
nonn
AUTHOR
Omar E. Pol, Oct 07 2011
STATUS
approved