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%I #54 Dec 16 2020 06:19:26
%S 1,1,1,1,1,1,1,1,1,1,1,2,3,4,4,4,4,4,4,4,4,4,5,7,10,12,13,13,13,13,13,
%T 13,13,14,16,21,27,32,34,35,35,35,35,35,36,38,44,54,67,77,83,85,86,86,
%U 86,87,89,95,107,128,152,173,185,191,193,194,195
%N Column 10 of square array A195825. Also column 1 of triangle A210954. Also 1 together with the row sums of triangle A210954
%C Note that this sequence contains five plateaus: [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [4, 4, 4, 4, 4, 4, 4, 4, 4], [13, 13, 13, 13, 13, 13, 13], [35, 35, 35, 35, 35], [86, 86, 86]. For more information see A210843 and other sequences of this family. - _Omar E. Pol_, Jun 29 2012
%H Seiichi Manyama, <a href="/A210964/b210964.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..3000 from Vaclav Kotesovec)
%H Vaclav Kotesovec, <a href="/A210964/a210964.jpg">Graph - The asymptotic ratio</a>
%H Michael Somos, <a href="/A010815/a010815.txt">Introduction to Ramanujan theta functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujanThetaFunctions.html">Ramanujan Theta Functions</a>
%F Expansion of 1 / f(-x, -x^11) in powers of x where f() is a Ramanujan theta function. - _Michael Somos_, Jan 10 2015
%F Partitions of n into parts of the form 12*k, 12*k+1, 12*k+11. - _Michael Somos_, Jan 10 2015
%F Euler transform of period 12 sequence [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, ...]. - _Michael Somos_, Jan 10 2015
%F G.f.: Product_{k>0} 1 / ((1 - x^(12*k)) * (1 - x^(12*k - 1)) * (1 - x^(12*k - 11))).
%F Convolution inverse of A247133.
%F a(n) ~ sqrt(2)*(1+sqrt(3)) * exp(Pi*sqrt(n/6)) / (8*n). - _Vaclav Kotesovec_, Nov 08 2015
%F a(n) = (1/n)*Sum_{k=1..n} A284372(k)*a(n-k), a(0) = 1. - _Seiichi Manyama_, Mar 25 2017
%F a(n) = a(n-1) + a(n-11) - a(n-14) - a(n-34) + + - - (with the convention a(n) = 0 for negative n), where 1, 11, 14, 34, ... is the sequence of generalized 14-gonal numbers A195818. - _Peter Bala_, Dec 10 2020
%t nmax = 100; CoefficientList[Series[Product[1 / ((1 - x^(12*k)) * (1 - x^(12*k-1)) * (1 - x^(12*k-11))), {k, 1, nmax}], {x, 0, nmax}], x] (* _Vaclav Kotesovec_, Nov 08 2015 *)
%o (GWbasic)' A program with two A-numbers:
%o 10 Dim A195818(100), A057077(100), a(100): a(0)=1
%o 20 For n = 1 to 67: For j = 1 to n
%o 30 If A195818(j) <= n then a(n) = a(n) + A057077(j-1)*a(n - A195818(j))
%o 40 Next j: Print a(n-1); : Next n
%o 50 End
%Y Cf. A000041, A006950, A036820, A057077, A195818, A195825, A195848, A195849, A195850, A195851, A195852, A196933, A210944, A210954, A211970, A211971.
%Y Cf. A247133.
%K nonn
%O 0,12
%A _Omar E. Pol_, Jun 16 2012
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