A195851 Column 7 of array A195825. Also column 1 of triangle A195841. Also 1 together with the row sums of triangle A195841.

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

Links

Table of n, a(n) for n=0..60.

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

(GWbasic)' 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
' Omar E. Pol, Jun 10 2012

Crossrefs

Cf. A000041, A001082, A006950, A036820, A057077, A195160, A195831, A195825, A195848, A195849, A195850, A195852, A196933, A210964, A211971.

Sequence in context: A122815 A316942 A029127 * A369149 A131754 A287422

Adjacent sequences: A195848 A195849 A195850 * A195852 A195853 A195854

Keyword

nonn

Author

Omar E. Pol, Oct 07 2011

Status

approved