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A172369 Triangle t(n,k) read by rows: tretranomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of a generalized tetranacci sequence with multiplier m=3. 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 1, 7, 28, 28, 28, 7, 1, 1, 10, 70, 280, 280, 70, 10, 1, 1, 13, 130, 910, 3640, 910, 130, 13, 1, 1, 25, 325, 3250, 22750, 22750, 3250, 325, 25, 1, 1, 46, 1150, 14950, 149500, 261625, 149500, 14950, 1150, 46, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,17

COMMENTS

Start from the generalized tetranacci sequence A143454 and its partial products c(n) = 1, 1, 1, 1, 1, 4, 28, 280, 3640, 91000, 4186000,... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 3, 4, 5, 18, 100, 722, 5748, 52702, 592919,....

Note that rows n>=16 contain fractions. - R. J. Mathar, Jul 05 2012

LINKS

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

EXAMPLE

1;

1, 1;

1, 1, 1;

1, 1, 1, 1;

1, 1, 1, 1, 1;

1, 4, 4, 4, 4, 1;

1, 7, 28, 28, 28, 7, 1;

1, 10, 70, 280, 280, 70, 10, 1;

1, 13, 130, 910, 3640, 910, 130, 13, 1;

1, 25, 325, 3250, 22750, 22750, 3250, 325, 25, 1;

1, 46, 1150, 14950, 149500, 261625, 149500, 14950, 1150, 46, 1;

MATHEMATICA

Clear[f, c, a, t];

f[0, a_] := 0; f[1, a_] := 1; f[2, a_] := 1; f[3, a_] := 1;

f[n_, a_] := f[n, a] = a*f[n - 1, a] + f[n - 4, a]; (* position of a appears to be wrong *)

c[n_, a_] := If[n == 0, 1, Product[f[i, a], {i, 1, n}]];

t[n_, m_, a_] := c[n, a]/(c[m, a]*c[n - m, a]);

Table[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}], {a, 1, 10}];

Table[Flatten[Table[Table[t[n, m, a], {m, 0, n}], {n, 0, 10}]], {a, 1, 10}]

CROSSREFS

Sequence in context: A279406 A171408 A071907 * A190338 A199177 A320086

Adjacent sequences:  A172366 A172367 A172368 * A172370 A172371 A172372

KEYWORD

nonn,tabl,less

AUTHOR

Roger L. Bagula, Feb 01 2010

STATUS

approved

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Last modified September 19 15:24 EDT 2019. Contains 327198 sequences. (Running on oeis4.)