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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.

%I A195851 #38 May 17 2024 15:24:17
%S A195851 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,
%T A195851 34,35,35,36,38,44,54,67,77,83,85,87,89,95,107,128,152,173,185,192,
%U A195851 196,203,216,242,281,328,367,394,409,421,436,465
%N A195851 Column 7 of array A195825. Also column 1 of triangle A195841. Also 1 together with the row sums of triangle A195841.
%C A195851 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
%F A195851 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
%F A195851 a(n) ~ exp(Pi*sqrt(2*n)/3) / (8*sin(Pi/9)*n). - _Vaclav Kotesovec_, Aug 14 2017
%p A195851 A195160 := proc(n)
%p A195851         (18*n*(n+1)+5*(2*n+1)*(-1)^n-5)/16 ;
%p A195851 end proc:
%p A195851 A195841 := proc(n, k)
%p A195851         option remember;
%p A195851         local ks, a, j ;
%p A195851         if A195160(k) > n then
%p A195851                 0 ;
%p A195851         elif n <= 5 then
%p A195851                 return 1;
%p A195851         elif k = 1 then
%p A195851                 a := 0 ;
%p A195851                 for j from 1 do
%p A195851                         if A195160(j) <= n-1 then
%p A195851                                 a := a+procname(n-1, j) ;
%p A195851                         else
%p A195851                                 break;
%p A195851                         end if;
%p A195851                 end do;
%p A195851                 return a;
%p A195851         else
%p A195851                 ks := A195160(k) ;
%p A195851                 (-1)^floor((k-1)/2)*procname(n-ks+1, 1) ;
%p A195851         end if;
%p A195851 end proc:
%p A195851 A195851 := proc(n)
%p A195851         A195841(n+1,1) ;
%p A195851 end proc:
%p A195851 seq(A195851(n), n=0..60) ; # _R. J. Mathar_, Oct 08 2011
%o A195851 (GW-BASIC)' A program with two A-numbers:
%o A195851 10 Dim A195160(100), A057077(100), a(100): a(0)=1
%o A195851 20 For n = 1 to 61: For j = 1 to n
%o A195851 30 If A195160(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A195160(j))
%o A195851 40 Next j: Print a(n-1); : Next n
%o A195851 50 '_Omar E. Pol_, Jun 10 2012
%Y A195851 Cf. A000041, A001082, A006950, A036820, A057077, A195160, A195831, A195825, A195848, A195849, A195850, A195852, A196933, A210964, A211971.
%K A195851 nonn
%O A195851 0,9
%A A195851 _Omar E. Pol_, Oct 07 2011