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A172356 Fourth (second cubic) type of beta integer triangle sequence: a=1;f(n,a)=a*f(n-1,a)+f(n-3,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)) 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 3, 6, 6, 3, 1, 1, 4, 12, 24, 12, 4, 1, 1, 6, 24, 72, 72, 24, 6, 1, 1, 9, 54, 216, 324, 216, 54, 9, 1, 1, 13, 117, 702, 1404, 1404, 702, 117, 13, 1, 1, 19, 247, 2223, 6669, 8892, 6669, 2223, 247, 19, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

Row sums are:

{1, 2, 3, 4, 8, 20, 58, 206, 884, 4474, 27210,...}.

LINKS

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

FORMULA

a=1;

f(n,a)=a*f(n-1,a)+a*f(n-3,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))

EXAMPLE

{1},

{1, 1},

{1, 1, 1},

{1, 1, 1, 1},

{1, 2, 2, 2, 1},

{1, 3, 6, 6, 3, 1},

{1, 4, 12, 24, 12, 4, 1},

{1, 6, 24, 72, 72, 24, 6, 1},

{1, 9, 54, 216, 324, 216, 54, 9, 1},

{1, 13, 117, 702, 1404, 1404, 702, 117, 13, 1},

{1, 19, 247, 2223, 6669, 8892, 6669, 2223, 247, 19, 1}

MATHEMATICA

Clear[f, c, a, t];

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

f[n_, a_] := f[n, a] = a*f[n - 1, a] + f[n - 3, 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

cf. A010048

Sequence in context: A128084 A131823 A089722 * A184948 A242775 A079562

Adjacent sequences:  A172353 A172354 A172355 * A172357 A172358 A172359

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 01 2010

STATUS

approved

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Last modified March 26 12:43 EDT 2019. Contains 321497 sequences. (Running on oeis4.)