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A174448 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]]] 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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.

LINKS

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

FORMULA

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]]]

EXAMPLE

{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}

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: A330885 A255741 A132892 * A077028 A114225 A193515

Adjacent sequences:  A174445 A174446 A174447 * A174449 A174450 A174451

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Mar 20 2010

STATUS

approved

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Last modified April 13 06:02 EDT 2021. Contains 342935 sequences. (Running on oeis4.)