A152655 A vector recursion sequence: k = -3; m = 3; l = -3; a(n)=k*{0,a(n-2),0}+m*{-(m-1)/m,a(n-1)}++m*{a(n-1),-(m-1)/m}+l*{0,0,a(n-4),0,0}.

1, 1, 1, 1, 3, 1, 1, 9, 9, 1, 1, 27, 42, 27, 1, 1, 81, 177, 177, 81, 1, 1, 243, 690, 927, 690, 243, 1, 1, 729, 2553, 4293, 4293, 2553, 729, 1, 1, 2187, 9114, 18387, 22851, 18387, 9114, 2187, 1, 1, 6561, 31713, 74601, 110304, 110304, 74601, 31713, 6561, 1, 1

Offset

0,5

Comments

The row sums are:

{1, 2, 5, 20, 98, 518, 2795, 15152, 82229, 446360, 2423084,...}

Links

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

Formula

k = -3; m = 3; l = -3; a(n)=k*{0,a(n-2),0}+m*{-(m-1)/m,a(n-1)}++m*{a(n-1),-(m-1)/m}+l*{0,0,a(n-4),0,0}.

Example

{1},
{1, 1},
{1, 3, 1},
{1, 9, 9, 1},
{1, 27, 42, 27, 1},
{1, 81, 177, 177, 81, 1},
{1, 243, 690, 927, 690, 243, 1},
{1, 729, 2553, 4293, 4293, 2553, 729, 1},
{1, 2187, 9114, 18387, 22851, 18387, 9114, 2187, 1},
{1, 6561, 31713, 74601, 110304, 110304, 74601, 31713, 6561, 1},
{1, 19683, 108258, 290871, 497484, 590490, 497484, 290871, 108258, 19683, 1}

Mathematica

Clear[a, k, m, l]; k = -3; m = 3; l = -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}] +
If[n >= 4, k*Join[{0, 0}, a[n - 4], {0, 0}], Table[0, {i, 0, n}]];
Table[a[n], {n, 0, 10}]; Flatten[%]

Crossrefs

Sequence in context: A156610 A203460 A157179 * A144493 A118180 A176482

Adjacent sequences: A152652 A152653 A152654 * A152656 A152657 A152658

Keyword

nonn,uned

Author

Roger L. Bagula, Dec 10 2008

Status

approved