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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(binomial(n,q)/2)? - Clark Kimberling, Jul 30 2011 LINKS 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 19:53 EDT 2019. Contains 328319 sequences. (Running on oeis4.)