A152860 Scaled row sum zero vector recursion:s=3; v(n)={s^(n+1),s^(n+1)-Sum[s^i,{i,2,n}],s^n,...,-1}.

1, 1, -1, 3, -2, -1, 9, -5, -3, -1, 27, -14, -9, -3, -1, 81, -41, -27, -9, -3, -1, 243, -122, -81, -27, -9, -3, -1, 729, -365, -243, -81, -27, -9, -3, -1, 2187, -1094, -729, -243, -81, -27, -9, -3, -1, 6561, -3281, -2187, -729, -243, -81, -27, -9, -3, -1, 19683

Offset

0,4

Links

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

Formula

s = 3; v(n) = {s^(n+1),s^(n+1)-Sum[s^i,{i,2,n}],s^n,...,-1}.

Example

{1},
{1, -1},
{3, -2, -1},
{9, -5, -3, -1},
{27, -14, -9, -3, -1},
{81, -41, -27, -9, -3, -1},
{243, -122, -81, -27, -9, -3, -1},
{729, -365, -243, -81, -27, -9, -3, -1},
{2187, -1094, -729, -243, -81, -27, -9, -3, -1},
{6561, -3281, -2187, -729, -243, -81, -27, -9, -3, -1},
{19683, -9842, -6561, -2187, -729, -243, -81, -27, -9, -3, -1}

Mathematica

Clear[s, b, n]; s = 3; b[0] = {1}; b[1] = {1, -1};
b[n_] := Join[{s^(n + 1)}, -{s^(n + 1) - Sum[s^i, {i, n, 2, -1}]}, -Table[s^i, {i, n, 2, -1}]]/9;
Table[b[n], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A183154 A193791 A160760 * A002350 A109267 A185416

Adjacent sequences: A152857 A152858 A152859 * A152861 A152862 A152863

Keyword

sign

Author

Roger L. Bagula, Dec 14 2008

Status

approved