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 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}]. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 12 00:34 EDT 2022. Contains 356067 sequences. (Running on oeis4.)