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Search: id:A122073
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| A122073 |
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Triangular array from Steinbach matrices plus their squares as characteristic polynomials: M[i,j]=A[i,j]+A[i,j]^2: A[i,j]^2=Min[i,j]; CharacteristicPolynomial[M[i,j]];. |
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+0
1
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| 1, 2, -1, 0, -4, 1, 2, -9, 8, -1, -2, -3, 19, -12, 1, -4, -6, 47, -55, 18, -1, 2, 15, 0, -88, 93, -24, 1, 2, 23, -7, -190, 324, -182, 32, -1, 0, -12, -63, 62, 332, -554, 274, -40, 1, 2, -9, -108, 133, 678, -1642, 1346, -450, 50, -1, -2, -11, 55, 276, -463, -1129, 2832, -2128, 630, -60, 1, -4, -30, 71, 543, -1044, -2204, 7761
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Based on the idea that the Steinbach matrices form a "golden Field". Matrices are: {{2, 2}, {2, 2}}, {{2, 2, 2}, {2, 3, 2}, {2, 2, 3}}, {{2, 2, 2, 2}, {2, 3, 3, 2}, {2, 3, 3, 3}, {2, 2, 3, 4}}, {{2, 2, 2, 2, 2}, {2, 3, 3, 3, 2}, {2, 3, 4, 3, 3}, {2, 3, 3, 4, 4}, {2, 2, 3, 4, 5}}, {{2, 2, 2, 2, 2, 2}, {2,3, 3, 3, 3, 2}, {2, 3, 4, 4, 3, 3}, {2, 3, 4, 4, 4, 4}, {2, 3, 3, 4, 5, 5}, {2, 2, 3, 4, 5, 6}}
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REFERENCES
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Peter Steinbach, "Golden Fields: A Case for the Heptagon", Mathematics Magazine, Vol. 70, No. 1, Feb. 1997.
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FORMULA
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dth level M(i,j)->An[d]; T(n,m)=CoefficientList[CharacteristicPolynomial[An[d], x], x]
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EXAMPLE
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{1},
{2, -1},
{0, -4, 1},
{2, -9, 8, -1},
{-2, -3, 19, -12, 1},
{-4, -6,47, -55, 18, -1}
{2, 15, 0, -88, 93, -24, 1},
{2, 23, -7, -190, 324, -182, 32, -1},
{0, -12, -63, 62, 332, -554, 274, -40, 1}
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MATHEMATICA
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An[d_] := Table[Min[n, m] + If[n + m - 1 > d, 0, 1], {n, 1, d}, {m, 1, d}]; Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]
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CROSSREFS
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Cf. A038223, A038223, A076756, A054142.
Sequence in context: A143425 A166555 A136329 this_sequence A106236 A122792 A139136
Adjacent sequences: A122070 A122071 A122072 this_sequence A122074 A122075 A122076
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KEYWORD
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tabl,uned,sign
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AUTHOR
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Gary Adamson (qntmpkt(AT)yahoo.com), Oct 16 2006
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