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A174448 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 = 12, read by rows. 3
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, 1, 7, 33, 99, 197, 275, 275, 197, 99, 33, 7, 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 = 12.

EXAMPLE

Triangle begins as:

  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[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, 12], {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, 12): 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, 12) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Aug 05 2021

CROSSREFS

Cf. A174446 (q=1), A174447 (q=4), this sequence (q=12).

Sequence in context: A330885 A255741 A132892 * A077028 A114225 A193515

Adjacent sequences:  A174445 A174446 A174447 * A174449 A174450 A174451

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 December 6 04:20 EST 2021. Contains 349562 sequences. (Running on oeis4.)