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Search: id:A135256
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| A135256 |
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A triangular sequence based on a further generalization of the Cornelius-Schultz matrix polynomials to two sequences in i and j. a(n)=(n-1)!/f[n]: f[n]-> Fibonacci numbers; c(n)=1/n; B(i,j)=(-1)^(i + j)*a[j + 1]*c[i + 1]/(j!*(i - j)!) as a lower triangular matrix. |
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| 1, 2, -1, 12, -8, 1, 144, -108, 20, -1, 3600, -2844, 608, -45, 1, 172800, -140112, 32028, -2768, 93, -1, 15724800, -12922992, 3054660, -283916, 11231, -184, 1, 2641766400, -2186787456, 526105872, -50752548, 2170724, -42143, 352, -1, 808380518400, -671798727936, 163175184288, -16056385560
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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This result is a product of emails and my own work between Dr. Cornelius
and Dr. Schultz and Gary Adamson and myself. I have been trying to
see how the tridiagonal Heisenberg matrices could be related to this new formal type. Gary Adamson and I did some work in late 2006 on tridiagonal matrix forms
and their polynomials as related to triangular sequences like this one.
This two sequence form of the Cornelius-Schultz matrix seems to be a new type that is complexity equivalent to the symmetrical tridiagonal matrices.
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LINKS
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E. F. Cornelius Jr. and P. Schultz, Sequences generated by polynomials, Amer. Math. Monthly, No. 2, 2008.
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FORMULA
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a(n)=(n-1)!/f[n]: f[n]-> Fibonacci numbers; c(n)=1/n; B(i,j)=(-1)^(i + j)*a[j + 1]*c[i + 1]/(j!*(i - j)!) as lower trianular t(n,m)=Coefficients of characteristic polynomials of the inverse of B(i,j)
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EXAMPLE
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{1},
{2, -1},
{12, -8, 1},
{144, -108,20, -1},
{3600, -2844, 608, -45, 1},
{172800, -140112, 32028, -2768, 93, -1},
{15724800, -12922992, 3054660, -283916, 11231, -184, 1}
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CROSSREFS
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Sequence in context: A128413 A058843 A130559 this_sequence A090586 A048854 A151508
Adjacent sequences: A135253 A135254 A135255 this_sequence A135257 A135258 A135259
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 13 2008
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