A158418 A triangle sequence from matrix polynomials of a three symbol type {0, 1, 2}: c(i,k)= Floor[Mod[i/2^k, 2]]; M(d)=Table[If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 0, 1, If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 1, 2, 0]], {n, 0, d - 1}, {m, 0, d - 1}].

1, 1, -1, 1, -3, 1, 1, -5, 5, -1, -3, 11, -4, -5, 1, -3, 17, -18, -2, 7, -1, 9, -39, 12, 35, -12, -7, 1, -27, 81, 54, -104, -28, 30, 7, -1, -135, 621, -459, -286, 266, 58, -43, -7, 1, -135, 891, -1269, 155, 652, -216, -119, 37, 9, -1, 405, -2133, 1431, 1986, -1677

Offset

0,5

Comments

Row sums are:

{1, 2, 5, 12, 24, 48, 115, 332, 1876, 3484, 8969,...}.

Example matrix:

M(4)={{1, 1, 1, 1},

{1, 2, 1, 2},

{1, 1, 2, 2},

{1, 2, 2, 0}}.

Links

Table of n, a(n) for n=0..59.

Formula

c(i,k)= Floor[Mod[i/2^k, 2]];

m(d)=Table[If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 0, 1, If[Sum[c(n, k)*c(m, k), {k, 0, d - 1}] == 1, 2, 0]], {n, 0, d - 1}, {m, 0, d - 1}];

out_(n,m)=coefficient(characteristicpolynomial(M(n),x),x)

Example

{1},
{1, -1},
{1, -3, 1},
{1, -5, 5, -1},
{-3, 11, -4, -5, 1},
{-3, 17, -18, -2, 7, -1},
{9, -39, 12, 35, -12, -7, 1},
{-27, 81, 54, -104, -28, 30, 7, -1},
{-135, 621, -459, -286, 266, 58, -43, -7, 1},
{-135, 891, -1269, 155, 652, -216, -119, 37, 9, -1},
{405, -2133, 1431, 1986, -1677, -621, 543, 102, -61, -9, 1}

Mathematica

Clear[c, b, a, An];
c[i_, k_] := Floor[Mod[i/2^k, 2]];
An[d_] := Table[If[Sum[c[n, k]*c[m, k], {k, 0, d - 1}] == 0, 1, If[Sum[c[n, k]*c[m, k], {k, 0, d - 1}] == 1, 2, 0]], {n, 0, d - 1}, {m, 0, d - 1}];
Table[An[n], {n, 1, 10}];
a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[An[ d], x], x], {d, 1, 10}]] ;
Flatten[a]
RowSum = Table[Apply[Plus, Abs[a[[n]]]], {n, 1, Length[a]}];

Crossrefs

Sequence in context: A300966 A300923 A301531 * A124925 A073145 A245368

Adjacent sequences: A158415 A158416 A158417 * A158419 A158420 A158421

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 18 2009

Status

approved