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).

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

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