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Search: id:A099037
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| A099037 |
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Triangle of diagonals of symmetric Krawtchouk matrices. |
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+0
2
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| 1, 1, -1, 1, 0, 1, 1, 3, -3, -1, 1, 8, -12, 8, 1, 1, 15, -20, 20, -15, -1, 1, 24, -15, 0, -15, 24, 1, 1, 35, 21, -105, 105, -21, -35, -1, 1, 48, 112, -336, 420, -336, 112, 48, 1, 1, 63, 288, -672, 756, -756, 672, -288, -63, -1, 1, 80, 585, -960, 420, 0, 420, -960, 585, 80, 1, 1, 99, 1045, -825, -1980, 4620, -4620, 1980, 825
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Row sums have e.g.f. BesselI(0,2x) (A000984 with interpolated zeros). Diagonal sums are A099038.
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REFERENCES
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P. Feinsilver, R. Fitzgerald, The Spectrum of Symmetric Krawtchouk Matrices. Linear Algebra and Its Applications, Vol. 235 (1996), pp. 121-139
P. Feinsilver, J. Kocik, Krawtchouk matrices from classical and quantum walks. Contemporary Mathematics, 287 2001, pp. 83-96
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FORMULA
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Triangle T(n, k)=if(k<=n, C(n, k)*sum{i=0..n, (-1)^i*C(k, i)C(n-k, k-i)}, 0)
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EXAMPLE
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Rows begin {1}, {1,-1}, {1,0,1}, {1,3,-3,1}, {1,8,-12,8,1},...
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CROSSREFS
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Cf. A098593.
Sequence in context: A075772 A119608 A101842 this_sequence A104378 A075837 A087107
Adjacent sequences: A099034 A099035 A099036 this_sequence A099038 A099039 A099040
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 23 2004
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