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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. 17
 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 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

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Last modified May 28 13:05 EDT 2022. Contains 354115 sequences. (Running on oeis4.)