A195849 Column 5 of array A195825. Also column 1 of triangle A195839. Also 1 together with the row sums of triangle A195839.

1, 1, 1, 1, 1, 1, 2, 3, 4, 4, 4, 4, 5, 7, 10, 12, 13, 13, 14, 16, 21, 27, 32, 34, 36, 38, 44, 54, 67, 77, 84, 88, 95, 107, 128, 152, 174, 188, 200, 215, 242, 281, 329, 370, 402, 428, 462, 513, 589, 674, 754, 816, 873, 940, 1041, 1176, 1333, 1477, 1600, 1710, 1845

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

From Omar E. Pol, Jun 10 2012: (Start)
(GWbasic)' A program with two A-numbers:
10 Dim A118277(100), A057077(100), a(100): a(0)=1
20 For n = 1 to 61: For j = 1 to n
30 If A118277(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A118277(j))
40 Next j: Print a(n-1); : Next n (End)

Crossrefs

Cf. A000041, A001082, A006950, A036820, A057077, A118277, A195825, A195829, A195839, A195848, A195850, A195851, A195852, A196933, A210843, A210964, A211971.

Sequence in context: A120509 A029106 A064004 * A087827 A136528 A263252

Adjacent sequences: A195846 A195847 A195848 * A195850 A195851 A195852

Keyword

nonn

Author

Omar E. Pol, Oct 07 2011

Status

approved