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A153489 Triangular recursive sequence: a(n,k)=(n - k + 1)A(n - 1, k - 1) + (k)* A(n - 1, k) - 18*A(n - 2, k - 1). 0
2, 3, 3, 2, 14, 2, 2, 25, 25, 2, 2, 49, 60, 49, 2, 2, 115, 126, 126, 115, 2, 2, 217, 253, 514, 253, 217, 2, 2, 415, 506, 1264, 1264, 506, 415, 2, 2, 810, 517, 3538, 3388, 3538, 517, 810, 2, 2, 1602, 561, 8663, 15416, 15416, 8663, 561, 1602, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Row sums are:

{2, 6, 18, 54, 162, 486, 1458, 4374, 13122, 52488,...}.

LINKS

Table of n, a(n) for n=1..55.

FORMULA

a(n,k)=(n - k + 1)A(n - 1, k - 1) + (k)* A(n - 1, k) - 18*A(n - 2, k - 1).

EXAMPLE

{2},

{3, 3},

{2, 14, 2},

{2, 25, 25, 2},

{2, 49, 60, 49, 2},

{2, 115, 126, 126, 115, 2},

{2, 217, 253, 514, 253, 217, 2},

{2, 415, 506, 1264, 1264, 506, 415, 2},

{2, 810, 517, 3538, 3388, 3538, 517, 810, 2},

{2, 1602, 561, 8663, 15416, 15416, 8663, 561, 1602, 2}

MATHEMATICA

Clear[t, n, m, A];

A[2, 1] := A[2, 2] = 3;

A[3, 2] = 14;

A[4, 2] = 25; A[4, 3] = 25;

A[5, 2] = 49; A[5, 3] = 60; A[5, 4] = 49;

A[6, 2] = 115; A[6, 3] = 126; A[6, 4] = 126; A[6, 5] = 115;

A[7, 2] = 217; A[7, 3] = 253; A[7, 4] = 514; A[7, 5] = 253; A[7, 6] = 217;

A[8, 2] = 415; A[8, 3] = 506; A[8, 4] = 1264; A[8, 5] = 1264; A[8, 6] = 506; A[8, 7] = 415;

A[n_, 1] := 2; A[n_, n_] := 2;

A[n_, k_] := (n - k + 1)A[n - 1, k - 1] + (k)* A[n - 1, k] - 18*A[ n - 2, k - 1];

Table[Table[A[n, m], {m, 1, n}], {n, 1, 10}]

Flatten[%] Table[Sum[A[n, m], {m, 1, n}], {n, 1, 10}];

Table[Sum[A[n, m], {m, 1, n}]/(2*3^(n - 1)), {n, 1, 10}]:

CROSSREFS

Sequence in context: A153283 A153288 A153479 * A153310 A155688 A215490

Adjacent sequences:  A153486 A153487 A153488 * A153490 A153491 A153492

KEYWORD

nonn,uned,tabl

AUTHOR

Roger L. Bagula, Dec 27 2008

STATUS

approved

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Last modified May 6 17:27 EDT 2021. Contains 343586 sequences. (Running on oeis4.)