A152613 A new vector recursion sequence: a(n)=-2*{0,a(n-2),0}+3*{-2/3,a(n-1)}+3*{a(n-1),-2/2}.

1, 1, 1, 1, 4, 1, 1, 13, 13, 1, 1, 40, 70, 40, 1, 1, 121, 304, 304, 121, 1, 1, 364, 1195, 1684, 1195, 364, 1, 1, 1093, 4435, 8029, 8029, 4435, 1093, 1, 1, 3280, 15856, 35002, 44806, 35002, 15856, 3280, 1, 1, 9841, 55222, 143704, 223366, 223366, 143704, 55222, 9841

Offset

0,5

Links

Table of n, a(n) for n=0..53.

Formula

a(n)=-2*{0,a(n-2),0}+3*{-2/3,a(n-1)}+3*{a(n-1),-2/2}.

Example

{1},
{1, 1},
{1, 4, 1},
{1, 13, 13, 1},
{1, 40, 70, 40, 1},
{1, 121, 304, 304, 121, 1},
{1, 364, 1195, 1684, 1195, 364, 1},
{1, 1093, 4435, 8029, 8029, 4435, 1093, 1},
{1, 3280, 15856, 35002, 44806, 35002, 15856, 3280, 1},
{1, 9841, 55222, 143704, 223366, 223366, 143704, 55222, 9841, 1},
{1, 29524, 188629, 565066, 1031206, 1250584, 1031206, 565066, 188629, 29524, 1}

Mathematica

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

Crossrefs

Sequence in context: A179086 A255494 A146956 * A157153 A212801 A147565

Adjacent sequences: A152610 A152611 A152612 * A152614 A152615 A152616

Keyword

nonn,uned,tabl

Author

Roger L. Bagula, Dec 09 2008

Status

approved