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A195849 Column 5 of array A195825. Also column 1 of triangle A195839. Also 1 together with the row sums of triangle A195839. 15
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 (list; graph; refs; listen; history; text; internal format)
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

LINKS

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

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

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

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Last modified April 5 20:15 EDT 2020. Contains 333260 sequences. (Running on oeis4.)