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%I #48 Dec 16 2020 06:19:04
%S 1,1,1,1,1,1,1,2,3,4,4,4,4,4,5,7,10,12,13,13,13,14,16,21,27,32,34,35,
%T 36,38,44,54,67,77,83,86,89,95,107,128,152,173,186,194,202,216,242,
%U 281,328,368,396,415,434,464,514,588,672,748,803,844
%N Column 6 of array A195825. Also column 1 of triangle A195840. Also 1 together with the row sums of triangle A195840.
%C Note that this sequence contains three plateaus: [1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4], [13, 13, 13]. For more information see A210843 and other sequences of this family. - _Omar E. Pol_, Jun 29 2012
%C Number of partitions of n into parts congruent to 0, 1 or 7 (mod 8). - _Peter Bala_, Dec 10 2020
%F G.f.: Product_{k>=1} 1/((1 - x^(8*k))*(1 - x^(8*k-1))*(1 - x^(8*k-7))). - _Ilya Gutkovskiy_, Aug 13 2017
%F a(n) ~ exp(Pi*sqrt(n)/2) / (4*sqrt(2-sqrt(2))*n). - _Vaclav Kotesovec_, Aug 14 2017
%F a(n) = a(n-1) + a(n-7) - a(n-10) - a(n-22) + + - - (with the convention a(n) = 0 for negative n), where 1, 7, 10, 22, ... is the sequence of generalized 10-gonal numbers A074377. - _Peter Bala_, Dec 10 2020
%o (GWbasic)' A program with two A-numbers:
%o 10 Dim A074377(100), A057077(100), a(100): a(0)=1
%o 20 For n = 1 to 60: For j = 1 to n
%o 30 If A074377(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A074377(j))
%o 40 Next j: Print a(n-1); : Next n
%o ' _Omar E. Pol_, Jun 10 2012
%Y Cf. A000041, A001082, A006950, A036820, A057077, A074377, A195825, A195830, A195848, A195849, A195851, A195852, A196933, A210964, A211971.
%K nonn,easy
%O 0,8
%A _Omar E. Pol_, Oct 07 2011
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