

A174446


A symmetrical triangle sequence: q=1; f(n,q) = 1 + tanh((n1)/q; t(n,m,q)=If[n == 0 or n == 1, 1, Ceiling[Binomial[n, m]/f[n, q]]].


0



1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 4, 3, 1, 1, 3, 6, 6, 3, 1, 1, 4, 8, 11, 8, 4, 1, 1, 4, 11, 18, 18, 11, 4, 1, 1, 5, 15, 29, 36, 29, 15, 5, 1, 1, 5, 19, 43, 64, 64, 43, 19, 5, 1, 1, 6, 23, 61, 106, 127, 106, 61, 23, 6, 1
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OFFSET

0,5


COMMENTS

Row sums are {1, 2, 4, 6, 12, 20, 37, 68, 136, 264, 521, ...}.
Sequence is defined as attenuated or frictional combination that get weaker as n increases much like natural processes.
For what pairs (n,q) is f(n,q) = 1 + floor(binomial(n,q)/2)?  Clark Kimberling, Jul 30 2011


LINKS

Table of n, a(n) for n=0..65.


FORMULA

q=1;
f(n,q) = 1 + tanh((n1)/q);
t(n,m,q)=If[n == 0 or n == 1, 1, Ceiling[Binomial[n, m]/f[n, q]]]


EXAMPLE

{1},
{1, 1},
{1, 2, 1},
{1, 2, 2, 1},
{1, 3, 4, 3, 1},
{1, 3, 6, 6, 3, 1},
{1, 4, 8, 11, 8, 4, 1},
{1, 4, 11, 18, 18, 11, 4, 1},
{1, 5, 15, 29, 36, 29, 15, 5, 1},
{1, 5, 19, 43, 64, 64, 43, 19, 5, 1},
{1, 6, 23, 61, 106, 127, 106, 61, 23, 6, 1}


MATHEMATICA

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]]]


CROSSREFS

Sequence in context: A048570 A090806 A241926 * A071201 A318045 A240656
Adjacent sequences: A174443 A174444 A174445 * A174447 A174448 A174449


KEYWORD

nonn,tabl,uned


AUTHOR

Roger L. Bagula, Mar 20 2010


STATUS

approved



