A158417 A triangle sequence from matrix polynomials of a three symbol type {0, 1, -1}: 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, -1, 0]], {n, 0, d - 1}, {m, 0, d - 1}].

1, 1, -1, -2, 0, 1, 4, 4, -1, -1, 12, -4, -7, 1, 1, -24, -16, 18, 10, -2, -1, -72, 48, 66, -22, -15, 2, 1, -216, 432, -54, -158, 26, 21, -2, -1, 864, 0, -864, 128, 230, -32, -25, 2, 1, -1728, -1728, 1512, 1328, -542, -318, 73, 31, -3, -1, -5184, 1728, 7992, -1968

Offset

0,4

Comments

Row sums are:

{1, 2, 3, 10, 25, 71, 226, 910, 2146, 7264, 21842,...}.

Example matrix:

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

{1, -1, 1, -1},

{1, 1, -1, -1},

{1, -1, -1, 0}}.

Links

Table of n, a(n) for n=0..58.

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, -1, 0]], {n, 0, d - 1}, {m, 0, d - 1}];

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

Example

{1},
{1, -1},
{-2, 0, 1},
{4, 4, -1, -1},
{12, -4, -7, 1, 1},
{-24, -16, 18, 10, -2, -1},
{-72, 48, 66, -22, -15, 2, 1},
{-216, 432, -54, -158, 26, 21, -2, -1},
{864, 0, -864, 128, 230, -32, -25, 2, 1},
{-1728, -1728, 1512, 1328, -542, -318, 73, 31, -3, -1},
{-5184, 1728, 7992, -1968, -3522, 738, 579, -87, -40, 3, 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, -1, 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: A288515 A264583 A158984 * A139435 A077909 A247126

Adjacent sequences: A158414 A158415 A158416 * A158418 A158419 A158420

Keyword

sign,tabl,uned

Author

Roger L. Bagula, Mar 18 2009

Status

approved