A144493 Triangle read by rows. Let k=-3, m=3. Row n is a vector v(n) defined as follows: v(n)=k*{0,v(n-2),0}+m*{-(m-1)/m,v(n-1)}+m*{v(n-1),-(m-1)/m}.

1, 1, 1, 1, 3, 1, 1, 9, 9, 1, 1, 27, 45, 27, 1, 1, 81, 189, 189, 81, 1, 1, 243, 729, 999, 729, 243, 1, 1, 729, 2673, 4617, 4617, 2673, 729, 1, 1, 2187, 9477, 19683, 24705, 19683, 9477, 2187, 1, 1, 6561, 32805, 79461, 119313, 119313, 79461, 32805, 6561, 1, 1

Offset

0,5

Comments

Row sums are: {1, 2, 5, 20, 101, 542, 2945, 16040, 87401, 476282, 2595485...}.

Links

Table of n, a(n) for n=0..55.

Example

{1},
{1, 1},
{1, 3, 1},
{1, 9, 9, 1},
{1, 27, 45, 27, 1},
{1, 81, 189, 189, 81, 1},
{1, 243, 729, 999, 729, 243, 1},
{1, 729, 2673, 4617, 4617, 2673, 729, 1},
{1, 2187, 9477, 19683, 24705, 19683, 9477, 2187, 1},
{1, 6561, 32805, 79461, 119313, 119313, 79461, 32805, 6561, 1},
{1, 19683, 111537, 308367, 537273, 641763, 537273, 308367, 111537, 19683, 1}

Mathematica

Clear[a, k, m]; k = -3; m = 3; a[0] = {1}; a[1] = {1, 1};
a[n_] := a[n] = k*Join[{0}, a[n - 2], {0}] + m*Join[{-(m - 1)/m}, a[n - 1]] + m*Join[a[ n - 1], {-(m - 1)/m}];
Table[a[n], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A203460 A157179 A152655 * A118180 A176482 A045912

Adjacent sequences: A144490 A144491 A144492 * A144494 A144495 A144496

Keyword

nonn,tabl

Author

Roger L. Bagula, Dec 10 2008

Extensions

Edited by N. J. A. Sloane, Dec 11 2008

Status

approved