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A174446 A symmetrical triangle sequence:q=1;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, 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 (list; table; graph; refs; listen; history; text; internal format)
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(C(n,q)/2)? [From Clark Kimberling, Jul 30 2011]

LINKS

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

FORMULA

q=1;

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, 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

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Last modified October 22 21:09 EDT 2018. Contains 316505 sequences. (Running on oeis4.)