A152862 Triangle read by rows: vector recursion: s=5; v(n)={s^(n+1),s^(n+1)-Sum[s^i,{i,2,n}],s^n,...,-1}/s^2.

1, 1, -1, 5, -4, -1, 25, -19, -5, -1, 125, -94, -25, -5, -1, 625, -469, -125, -25, -5, -1, 3125, -2344, -625, -125, -25, -5, -1, 15625, -11719, -3125, -625, -125, -25, -5, -1, 78125, -58594, -15625, -3125, -625, -125, -25, -5, -1, 390625, -292969, -78125

Offset

0,4

Comments

Except for first row, row sums are zero.

Links

Table of n, a(n) for n=0..47.

Formula

s = 5; v(n) = {s^(n+1),s^(n+1)-Sum[s^i,{i,2,n}],s^n,...,-1}/s^2.

Example

{1},
{1, -1},
{5, -4, -1},
{25, -19, -5, -1},
{125, -94, -25, -5, -1},
{625, -469, -125, -25, -5, -1},
{3125, -2344, -625, -125, -25, -5, -1},
{15625, -11719, -3125, -625, -125, -25, -5, -1},
{78125, -58594, -15625, -3125, -625, -125, -25, -5, -1},
{390625, -292969, -78125, -15625, -3125, -625, -125, -25, -5, -1},
{1953125, -1464844, -390625, -78125, -15625, -3125, -625, -125, -25, -5, -1}

Mathematica

Clear[s, b, n]; s = 5; 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}]]/s^2;
Table[b[n], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A008955 A182824 A329120 * A348014 A108440 A102220

Adjacent sequences: A152859 A152860 A152861 * A152863 A152864 A152865

Keyword

tabl,sign

Author

Roger L. Bagula, Dec 14 2008

Status

approved