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A193631
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Augmentation of the triangle given by p(n,k)=(3+(-1)^k)/2 for 0<=k<=n. See Comments.
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1
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1, 2, 1, 4, 4, 5, 8, 12, 22, 17, 16, 32, 72, 88, 89, 32, 80, 208, 328, 474, 417, 64, 192, 560, 1056, 1836, 2364, 2253, 128, 448, 1440, 3120, 6168, 9684, 13038, 11937, 256, 1024, 3584, 8704, 19040, 34240, 54800, 71152, 66737, 512, 2304, 8704, 23296
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OFFSET
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0,2
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COMMENTS
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For an introduction to the unary operation "augmentation" as applied to triangular arrays or sequences of polynomials, see A193091.
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LINKS
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EXAMPLE
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First five rows of the triangle P=p(n,k):
2
2...1
2...1...2
2...1...2...1
2...1...2...1...2
1
2....1
4....4....5
8....12...22...17
16...32...72...88...89
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MATHEMATICA
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p[n_, k_] := (3 + (-1)^k)/2;
Table[p[n, k], {n, 0, 7}, {k, 0, n}]
m[n_] := Table[If[i <= j, p[n + 1 - i, j - i], 0], {i, n}, {j, n + 1}]
TableForm[m[4]]
w[0, 0] = 1; w[1, 0] = p[1, 0]; w[1, 1] = p[1, 1];
v[0] = w[0, 0]; v[1] = {w[1, 0], w[1, 1]};
v[n_] := v[n - 1].m[n]
TableForm[Table[v[n], {n, 0, 6}]] (* A193631 *)
Flatten[Table[v[n], {n, 0, 8}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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