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A174447 Triangle T(n, k, q) = ceiling(binomial(n, k)/f(n, q)) with T(0, 0) = 1, f(n, q) = 1 + tanh((n-1)/q), and q = 4, read by rows. 3
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 3, 4, 3, 1, 1, 3, 6, 6, 3, 1, 1, 4, 9, 11, 9, 4, 1, 1, 4, 12, 19, 19, 12, 4, 1, 1, 5, 15, 29, 37, 29, 15, 5, 1, 1, 5, 19, 43, 65, 65, 43, 19, 5, 1, 1, 6, 23, 61, 107, 128, 107, 61, 23, 6, 1, 1, 6, 28, 84, 167, 233, 233, 167, 84, 28, 6, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

FORMULA

T(n, k, q) = ceiling(binomial(n, k)/f(n, q)) with T(0, 0) = 1, f(n, q) = 1 + tanh((n-1)/q), and q = 4.

EXAMPLE

Triangle begins as:

  1;

  1, 1;

  1, 2,  1;

  1, 3,  3,  1;

  1, 3,  4,  3,   1;

  1, 3,  6,  6,   3,   1;

  1, 4,  9, 11,   9,   4,   1;

  1, 4, 12, 19,  19,  12,   4,  1;

  1, 5, 15, 29,  37,  29,  15,  5,  1;

  1, 5, 19, 43,  65,  65,  43, 19,  5, 1;

  1, 6, 23, 61, 107, 128, 107, 61, 23, 6, 1;

MATHEMATICA

f[n_, q_]= 1 + Tanh[(n-1)/q];

T[n_, k_, q_]= If[n==0, 1, Ceiling[Binomial[n, k]/f[n, q]]];

Table[T[n, k, 4], {n, 0, 12}, {k, 0, n}]//Flatten

PROG

(MAGMA)

T:= func< n, k, q | n eq 0 select 1 else Ceiling(Binomial(n, k)/(1 + Tanh((n-1)/q))) >;

[T(n, k, 4): k in [0..n], n in [0..12]]; // G. C. Greubel, Aug 05 2021

(Sage)

def T(n, k, q): return 1 if (n==0) else ceil(binomial(n, k)/(1 + tanh((n-1)/q)))

flatten([[T(n, k, 4) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Aug 05 2021

CROSSREFS

Cf. A174446 (q=1), this sequence (q=4), A174448 (q=12).

Sequence in context: A169946 A160832 A157458 * A174374 A242641 A027948

Adjacent sequences:  A174444 A174445 A174446 * A174448 A174449 A174450

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 20 2010

EXTENSIONS

Edited by G. C. Greubel, Aug 05 2021

STATUS

approved

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Last modified October 28 07:43 EDT 2021. Contains 348321 sequences. (Running on oeis4.)