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A156608
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A q-combination triangle sequence built of Cartan D_n polynomials: m=2;q=3; p(x,n)=CartanDn(x,n). t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]]; b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].
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1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, -1, 1, 1, 1, -2, 2, 2, -2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, -1, 2, 2, -1, 1, 1, 1, -2, 2, 2, -4, 2, 2, -2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, -1, 2, 2, -1, 2, 2, -1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,17
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COMMENTS
| Row sums are:
{1, 2, 1, 4, 3, 2, 10, 6, 2, 16, 9,...}.
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FORMULA
| m=2;q=3; p(x,n)=CartanDn(x,n);
t(n,k)=If[m == 0, n!, Product[p(m+1),k), {k, 1, n}]];
b(n,k,m)=If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])].
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EXAMPLE
| {1},
{1, 1},
{1, -1, 1},
{1, 1, 1, 1},
{1, 1, -1, 1, 1},
{1, -2, 2, 2, -2, 1},
{1, 1, 2, 2, 2, 1, 1},
{1, 1, -1, 2, 2, -1, 1, 1},
{1, -2, 2, 2, -4, 2, 2, -2, 1},
{1, 1, 2, 2, 2, 2, 2, 2, 1, 1},
{1, 1, -1, 2, 2, -1, 2, 2, -1, 1, 1}
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MATHEMATICA
| Clear[t, n, m, i, k, a, b];
T[n_, m_, d_] := If[ n == m, 2, If[(m == d && n == d - 2) || (n == d && m == d - 2), -1, If[(n == m - 1 || n == m + 1) && n <= d - 1 && m <= d - 1, -1, 0]]];
M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}];
p[x_, n_] := If[n == 0, 1, CharacteristicPolynomial[M[n], x]];
a0 = Table[p[x, n], {n, 0, 20}] /. x -> m + 1;
t[n_, m_] = If[m == 0, n!, Product[a0[[k]], {k, 1, n}]];
b[n_, k_, m_] = If[n == 0, 1, t[n, m]/(t[k, m]*t[n - k, m])];
Table[Flatten[Table[Table[b[n, k, m], {k, 0, n}], {n, 0, 10}]], {m, 0, 15}]
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CROSSREFS
| Sequence in context: A030368 A037805 A106825 * A112505 A104638 A057155
Adjacent sequences: A156605 A156606 A156607 * A156609 A156610 A156611
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KEYWORD
| sign,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 11 2009
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