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Search: id:A131219
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| A131219 |
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Algorithm for a triangular sequence of the product of a modulo 2 Pascal's triangle with an Hadamard-Silvester Gray code binary triangular sequence. |
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+0
1
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| 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1
(list; table; graph; listen)
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OFFSET
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1,1
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FORMULA
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b(n,m)=Mod[binomial[n,m],2] c(n,m)=Gray_Code(n,m) a(n,m) = b(n,m)*c(n,m)
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EXAMPLE
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{1},
{1, 1},
{1, 0, 1},
{1, 0, 0, 1},
{1, 0, 0, 0, 1},
{1, 1, 0, 0, 1, 1},
{1, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 1, 0, 0, 0, 0, 0, 0, 1, 1},
{1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1},
{1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}
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MATHEMATICA
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c[i_, k_] := Floor[Mod[i/2^k, 2]]; b[i_, k_] = If[c[i, k] == 0 && c[i, k + 1] == 0, 0, If[c[i, k] == 1 && c[i, k + 1] == 1, 0, 1]]; n = 15 a0 = Table[If[Sum[b[i, k]*b[j, k], {k, 0, n}] == 0, 1, 0], {j, 0, n}, {i, 0, n}]; ListDensityPlot[a0, Mesh -> False]; c = Delete[Table[Reverse[Table[a0[[n, l - n]], {n, 1, l - 1}]], {l, 1, Dimensions[a0][[1]] + 1}], 1]; Flatten[c]; Dimensions[c]; d = Table[Table[Mod[Binomial[n0, m], 2], {m, 0, n0}], {n0, 0, n}] e = Table[Table[c[[n0, m]]*d[[n0, m]], {m, 1, n0}], {n0, 1, n + 1}] Flatten[e]
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CROSSREFS
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Cf. A047999.
Sequence in context: A127972 A103451 A103452 this_sequence A127970 A140865 A114000
Adjacent sequences: A131216 A131217 A131218 this_sequence A131220 A131221 A131222
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 27 2007
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