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A195849
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Column 5 of array A195825. Also column 1 of triangle A195839. Also 1 together with the row sums of triangle A195839.
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15
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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)
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OFFSET
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0,7
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COMMENTS
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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
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LINKS
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Table of n, a(n) for n=0..60.
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FORMULA
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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
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MAPLE
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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
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MATHEMATICA
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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 *)
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PROG
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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)
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Omar E. Pol, Oct 07 2011
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STATUS
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approved
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