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A172364 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, 3, 3, 3, 1, 1, 10, 30, 30, 10, 1, 1, 31, 310, 930, 310, 31, 1, 1, 94, 2914, 29140, 29140, 2914, 94, 1, 1, 285, 26790, 830490, 2768300, 830490, 26790, 285, 1, 1, 865, 246525, 23173350, 239457950, 239457950, 23173350, 246525, 865, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Start from the generalized tetranacci sequence 0, 1, 1, 1, 3, 10, 31, 94, 285, 865, 2626, 7972, 24201.., f(n) = 3*f(n-1)+f(n-4), and its partial products c(n) = 1, 1, 1, 1, 3, 30, 930, 87420, 24914700, 21551215500.. Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 3, 4, 11, 82, 1614, 64298, 4483432, 525757382, 104749766604,...

Note that rows n>= 12 contain fractions. - R. J. Mathar, Jul 05 2012

LINKS

Table of n, a(n) for n=0..54.

EXAMPLE

1;

1, 1;

1, 1, 1;

1, 1, 1, 1;

1, 3, 3, 3, 1;

1, 10, 30, 30, 10, 1;

1, 31, 310, 930, 310, 31, 1;

1, 94, 2914, 29140, 29140, 2914, 94, 1;

1, 285, 26790, 830490, 2768300, 830490, 26790, 285, 1;

1, 865, 246525, 23173350, 239457950, 239457950, 23173350, 246525, 865, 1;

1, 2626, 2271490, 647374650, 20284405700, 62881657670, 20284405700, 647374650, 2271490, 2626, 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];

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: A135368 A172358 A119560 * A323596 A323375 A140366

Adjacent sequences:  A172361 A172362 A172363 * A172365 A172366 A172367

KEYWORD

nonn,tabl,less

AUTHOR

Roger L. Bagula, Feb 01 2010

STATUS

approved

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Last modified November 13 16:08 EST 2019. Contains 329106 sequences. (Running on oeis4.)