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A172363 Triangle t(n,k) read by rows: tretranomial ratios c(n)/(c(k)*c(n-k)) where c are partial products of tetranacci sequence A003269. 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 3, 6, 6, 6, 3, 1, 1, 4, 12, 24, 24, 12, 4, 1, 1, 5, 20, 60, 120, 60, 20, 5, 1, 1, 7, 35, 140, 420, 420, 140, 35, 7, 1, 1, 10, 70, 350, 1400, 2100, 1400, 350, 70, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,17

COMMENTS

Start from the generalized tetranacci sequence A003269 and its partial products c(n) = 1, 1, 1, 1, 1, 2, 6, 24, 120, 840, 8400,... Then t(n,k) = c(n)/(c(k)*c(n-k)).

Row sums are 1, 2, 3, 4, 5, 10, 26, 82, 292, 1206, 5762,...

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, 2, 2, 2, 2, 1;

1, 3, 6, 6, 6, 3, 1;

1, 4, 12, 24, 24, 12, 4, 1;

1, 5, 20, 60, 120, 60, 20, 5, 1;

1, 7, 35, 140, 420, 420, 140, 35, 7, 1;

1, 10, 70, 350, 1400, 2100, 1400, 350, 70, 10, 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: A037200 A263992 A180174 * A181877 A236472 A175357

Adjacent sequences:  A172360 A172361 A172362 * A172364 A172365 A172366

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Feb 01 2010

STATUS

approved

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Last modified October 21 22:47 EDT 2019. Contains 328315 sequences. (Running on oeis4.)