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A124022 Triangular sequence from the characteristic polynomials of the SL(n,Z)/ determinants {1,-1} type triantidiagonal 2 center with one upper, -1 side antidiagonal above and below: M(3)={{0, -1, 1}, {-1, 2, -1}, {2, -1, 0}}. 0
1, 1, -1, -1, 2, 1, -1, 4, 2, -1, 1, -6, -7, 2, 1, 1, -9, -12, 10, 2, -1, -1, 12, 26, -18, -13, 2, 1, -1, 16, 40, -52, -24, 16, 2, -1, 1, -20, -70, 86, 87, -30, -19, 2, 1, 1, -25, -100, 190, 150, -131, -36, 22, 2, -1, -1, 30, 155, -294, -403, 232, 184, -42, -25, 2, 1, -1, 36, 210, -553, -656, 736, 332, -246, -48, 28, 2, -1, 1, -42 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Matrices: {{1}}, {{-1, 1}, {2, -1}}, {{0, -1, 1}, {-1, 2, -1}, {2, -1, 0}}, {{0, 0, -1, 1}, {0, -1, 2, -1}, {-1, 2, -1, 0}, {2, -1, 0, 0}}, {{0, 0, 0, -1, 1}, {0, 0, -1, 2, -1}, {0, -1, 2, -1, 0}, {-1, 2, -1, 0, 0}, {2, -1, 0, 0,0}}

LINKS

Table of n, a(n) for n=1..80.

FORMULA

k=2; m(n,m,d)= = Table[If[n +m - 1 == d && n > 1, k, If[n + m == d, -1, If[n + m - 2 == d, -1, If[n == 1 && m == d, k - 1, 0]]]], {n, 1, d}, {m, 1, d}];

EXAMPLE

Triangular sequence:

{1},

{1, -1},

{-1, 2, 1},

{-1, 4, 2, -1},

{1, -6, -7, 2, 1},

{1, -9, -12, 10, 2, -1},

{-1, 12, 26, -18, -13, 2, 1},

{-1, 16, 40, -52, -24,16, 2, -1},

{1, -20, -70, 86, 87, -30, -19, 2, 1}

MATHEMATICA

k = 2; An[d_] := Table[If[n + m - 1 == d && n > 1, k, If[n + m == d, -1, If[n + m - 2 == d, -1, If[n == 1 &&m == d, k - 1, 0]]]], {n, 1, d}, {m, 1, d}]; Join[An[1], Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]

CROSSREFS

Sequence in context: A229706 A319421 A092479 * A098063 A209438 A106396

Adjacent sequences:  A124019 A124020 A124021 * A124023 A124024 A124025

KEYWORD

sign,tabl,uned

AUTHOR

Gary W. Adamson and Roger L. Bagula, Oct 31 2006

STATUS

approved

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Last modified April 3 17:03 EDT 2020. Contains 333197 sequences. (Running on oeis4.)