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A157155 A general three part recursion triangle sequence second type: m=4; A(n,k,m)= (m*(n - k) + 1)*A(n - 1, k - 1, m) + (m*k + 1)*A(n - 1, k, m) - m*k*(n - k)*A(n - 2, k - 1, m). 0
1, 1, 1, 1, 6, 1, 1, 31, 31, 1, 1, 156, 462, 156, 1, 1, 781, 5442, 5442, 781, 1, 1, 3906, 57263, 124860, 57263, 3906, 1, 1, 19531, 566153, 2335435, 2335435, 566153, 19531, 1, 1, 97656, 5396164, 38814088, 71413750, 38814088, 5396164, 97656, 1, 1, 488281 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

The row sums are:

{1, 2, 8, 64, 776, 12448, 247200, 5842240, 160029568, 4983622144, 173864905984,...}.

What I have done here is subtract a new symmetrical part

to the "zero start" Sierpinski -Pascal recursion at "down two" or n-2 in my notation:

m*k*(n - k)*A(n - 2, k - 1, m).

It uses the symmetrical k*(n-k) multiplier.

LINKS

Table of n, a(n) for n=0..46.

FORMULA

m=4;

A(n,k,m)= (m*(n - k) + 1)*A(n - 1, k - 1, m) +

(m*k + 1)*A(n - 1, k, m) -

m*k*(n - k)*A(n - 2, k - 1, m).

EXAMPLE

{1},

{1, 1},

{1, 6, 1},

{1, 31, 31, 1},

{1, 156, 462, 156, 1},

{1, 781, 5442, 5442, 781, 1},

{1, 3906, 57263, 124860, 57263, 3906, 1},

{1, 19531, 566153, 2335435, 2335435, 566153, 19531, 1},

{1, 97656, 5396164, 38814088, 71413750, 38814088, 5396164, 97656, 1},

{1, 488281, 50303764, 598724228, 1842294798, 1842294798, 598724228, 50303764, 488281, 1},

{1, 2441406, 462597165, 8788946344, 42560964818, 70235006516, 42560964818, 8788946344, 462597165, 2441406, 1}

MATHEMATICA

Clear[A, n, k, m];

A[n_, 0, m_] := 1;

A[n_, n_, m_] := 1;

A[n_, k_, m_] := (m*(n - k) + 1)*A[n - 1, k - 1, m] + (m* k + 1)*A[n - 1, k, m] - m*k*(n - k)*A[n - 2, k - 1, m];

Table[A[n, k, m], {m, 0, 10}, {n, 0, 10}, {k, 0, n}];

Table[Flatten[Table[Table[A[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 10}]

CROSSREFS

Sequence in context: A111578 A166349 A176429 * A022169 A156601 A178232

Adjacent sequences:  A157152 A157153 A157154 * A157156 A157157 A157158

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Feb 24 2009

STATUS

approved

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Last modified August 24 16:10 EDT 2019. Contains 326295 sequences. (Running on oeis4.)