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A174448
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A symmetrical triangle sequence:q=12;f(n,q)=1+Tanh((n-1)/q;t(n,m,q)=If[n == 0 or n == 1, 1, Ceiling[Binomial[n, m]/f[n, q]]]
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0
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 4, 1, 1, 4, 8, 8, 4, 1, 1, 5, 11, 15, 11, 5, 1, 1, 5, 15, 24, 24, 15, 5, 1, 1, 6, 19, 37, 46, 37, 19, 6, 1, 1, 6, 23, 54, 80, 80, 54, 23, 6, 1, 1, 7, 28, 74, 129, 155, 129, 74, 28, 7, 1
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OFFSET
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0,5
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COMMENTS
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Row sums are:
{1, 2, 4, 8, 15, 26, 49, 90, 172, 328, 633,...}.
Sequence is defined as attenuated or frictional combination that get weaker as n increases much like natural processes.
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LINKS
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Table of n, a(n) for n=0..65.
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FORMULA
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q=12;
f(n,q)=1+Tanh((n-1)/q;
t(n,m,q)=If[n == 0 or n == 1, 1, Ceiling[Binomial[n, m]/f[n, q]]]
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EXAMPLE
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{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 4, 5, 4, 1},
{1, 4, 8, 8, 4, 1},
{1, 5, 11, 15, 11, 5, 1},
{1, 5, 15, 24, 24, 15, 5, 1},
{1, 6, 19, 37, 46, 37, 19, 6, 1},
{1, 6, 23, 54, 80, 80, 54, 23, 6, 1},
{1, 7, 28, 74, 129, 155, 129, 74, 28, 7, 1}
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MATHEMATICA
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f[0, q_] := 1; f[1, q_] := 1;
f[n_, q_] = 1 + Tanh[(n - 1)/q];
t[n_, m_, q_] = If[n == 0 || n == 1, 1, Ceiling[Binomial[n, m]/f[n, q]]]
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CROSSREFS
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Sequence in context: A330885 A255741 A132892 * A077028 A114225 A193515
Adjacent sequences: A174445 A174446 A174447 * A174449 A174450 A174451
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula, Mar 20 2010
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STATUS
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approved
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