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Search: id:A119468
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| A119468 |
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Triangle read by rows: T(n,k)=sum{j=0..n-k, C(n,2j)*C(n-2j,k)}. |
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+0
4
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| 1, 1, 1, 2, 2, 1, 4, 6, 3, 1, 8, 16, 12, 4, 1, 16, 40, 40, 20, 5, 1, 32, 96, 120, 80, 30, 6, 1, 64, 224, 336, 280, 140, 42, 7, 1, 128, 512, 896, 896, 560, 224, 56, 8, 1, 256, 1152, 2304, 2688, 2016, 1008, 336, 72, 9, 1, 512, 2560, 5760, 7680, 6720, 4032, 1680, 480, 90, 10
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Product of Pascal's triangle A007318 and A119467. Row sums are A007051. Diagonal sums are A113225.
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FORMULA
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G.f.: (1-x-xy)/(1-2x-2x*y+2x^2*y+x^2*y^2); Number triangle T(n,k)=sum{j=0..n, C(n,j)*C(j,k)*(1+(-1)^(j-k))/2}.
Contribution from Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jan 25 2009: (Start)
Define matrix: A(n,m,k)=If[m < n, 1, -1];
p(x,k)=CharacteristicPolynomial[A[n,m,k],x];
then t(n,m)=coefficients(p(x,n)). (End)
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EXAMPLE
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{1},
{1, 1},
{2, 2, 1},
{4, 6, 3, 1},
{8, 16, 12, 4, 1},
{16, 40, 40, 20, 5, 1},
{32, 96, 120, 80, 30, 6, 1},
{64, 224, 336, 280, 140, 42, 7, 1},
{128, 512, 896, 896, 560, 224, 56, 8, 1},
{256, 1152, 2304, 2688, 2016, 1008, 336, 72, 9, 1},
{512, 2560, 5760, 7680, 6720, 4032, 1680, 480, 90, 10, 1}
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MATHEMATICA
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Contribution from Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Jan 25 2009: (Start)
A[k_] := Table[If[m < n, 1, -1], {m, k}, {n, k}];
a = Join[{{1}}, Table[(-1)^n*CoefficientList[CharacteristicPolynomial[A[n], x], x], {n, 1, 10}]];
Flatten[a] (End)
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CROSSREFS
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Sequence in context: A121484 A080928 A068957 this_sequence A091869 A112307 A111062
Adjacent sequences: A119465 A119466 A119467 this_sequence A119469 A119470 A119471
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 21 2006
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