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A131219 Algorithm for a triangular sequence of the product of a modulo 2 Pascal's triangle with an Hadamard-Silvester Gray code binary triangular sequence. 0
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; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..105.

FORMULA

b(n,m)=Mod[binomial[n,m],2] c(n,m)=Gray_Code(n,m) a(n,m) = b(n,m)*c(n,m)

EXAMPLE

{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}

MATHEMATICA

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]

CROSSREFS

Cf. A047999.

Sequence in context: A127972 A103451 A103452 * A127970 A158856 A154957

Adjacent sequences:  A131216 A131217 A131218 * A131220 A131221 A131222

KEYWORD

nonn,tabl,uned

AUTHOR

Roger L. Bagula, Sep 27 2007

STATUS

approved

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Last modified June 25 12:55 EDT 2019. Contains 324352 sequences. (Running on oeis4.)