A152654 A vector recursion sequence: k = 1; m = 2; l = 1; 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, 5, 1, 1, 13, 13, 1, 1, 29, 58, 29, 1, 1, 61, 188, 188, 61, 1, 1, 125, 528, 815, 528, 125, 1, 1, 253, 1368, 2887, 2887, 1368, 253, 1, 1, 509, 3368, 9067, 12421, 9067, 3368, 509, 1, 1, 1021, 8008, 26299, 46051, 46051, 26299, 8008, 1021, 1, 1, 2045, 18568

Offset

0,5

Comments

The row sums are:

{1, 2, 7, 28, 118, 500, 2123, 9018, 38311, 162760, 691472,...}

Links

Table of n, a(n) for n=0..57.

Formula

k = 1; m = 2; l = 1; 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, 5, 1},
{1, 13, 13, 1},
{1, 29, 58, 29, 1},
{1, 61, 188, 188, 61, 1},
{1, 125, 528, 815, 528, 125, 1},
{1, 253, 1368, 2887, 2887, 1368, 253, 1},
{1, 509, 3368, 9067, 12421, 9067, 3368, 509, 1},
{1, 1021, 8008, 26299, 46051, 46051, 26299, 8008, 1021, 1},
{1, 2045, 18568, 72107, 154295, 197440, 154295, 72107, 18568, 2045, 1}

Mathematica

Clear[a, k, m, l] k = 1; m = 2; l = 1; 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: A114123 A324009 A143007 * A176487 A272644 A157177

Adjacent sequences: A152651 A152652 A152653 * A152655 A152656 A152657

Keyword

nonn,uned

Author

Roger L. Bagula, Dec 10 2008

Status

approved