A152602 A symmetrical vector coefficient recursion sequence: a(n)=2*{0,a(n-2,0}+2*{-1/2,a(n-1)}+2*{a(n-1),-1/2}.

1, 1, 1, 1, 6, 1, 1, 16, 16, 1, 1, 36, 76, 36, 1, 1, 76, 256, 256, 76, 1, 1, 156, 736, 1176, 736, 156, 1, 1, 316, 1936, 4336, 4336, 1936, 316, 1, 1, 636, 4816, 14016, 19696, 14016, 4816, 636, 1, 1, 1276, 11536, 41536, 76096, 76096, 41536, 11536, 1276, 1, 1, 2556

Offset

0,5

Comments

The name contains an unmatched bracket. - Editors, Mar 13 2024

Row sums are;

{1, 2, 8, 34, 150, 666, 2962, 13178, 58634, 260890, 1160826,...}

Links

Table of n, a(n) for n=0..56.

Formula

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

T(n,k) = 2T(n-2,k-1)+2T(n-1,k-1)+2T(n-1,k), 0<k<n, n>1. T(n,0) = 2T(n-1,0)-1, n>1. T(n,n) = 2T(n-1,n-1)-1, n>1. Row sum recurrence: s(n)=5*s(n-1)-2*s(n-2)-2*s(n-3), s=sum_(k=0..n) T(n,k). [From R. J. Mathar, Dec 10 2008]

Example

{1},
{1, 1},
{1, 6, 1},
{1, 16, 16, 1},
{1, 36, 76, 36, 1},
{1, 76, 256, 256, 76, 1},
{1, 156, 736, 1176, 736, 156, 1},
{1, 316, 1936, 4336, 4336, 1936, 316, 1},
{1, 636, 4816, 14016, 19696, 14016, 4816, 636, 1},
{1, 1276, 11536, 41536, 76096, 76096, 41536, 11536, 1276, 1},
{1, 2556, 26896, 115776, 263296, 343776, 263296, 115776, 26896, 2556, 1}

Mathematica

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

Crossrefs

Sequence in context: A357156 A296963 A176560 * A119726 A103999 A154985

Adjacent sequences: A152599 A152600 A152601 * A152603 A152604 A152605

Keyword

nonn,uned,tabl,obsc

Author

Roger L. Bagula, Dec 09 2008

Status

approved