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A144383
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T(n,k) = [t^k] 1/(t^n + t + 1), square array read by ascending antidiagonals (n >= 1, k >= 0).
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2
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1, 1, -2, 1, -1, 4, 1, -1, 0, -8, 1, -1, 1, 1, 16, 1, -1, 1, -2, -1, -32, 1, -1, 1, -1, 3, 0, 64, 1, -1, 1, -1, 0, -4, 1, -128, 1, -1, 1, -1, 1, 1, 6, -1, 256, 1, -1, 1, -1, 1, -2, -2, -9, 0, -512, 1, -1, 1, -1, 1, -1, 3, 3, 13, 1, 1024, 1, -1, 1, -1, 1, -1, 0, -4, -3, -19, -1, -2048
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OFFSET
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1,3
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LINKS
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EXAMPLE
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Square array begins:
n\k | 0 1 2 3 4 5 6 7 8 9 ...
--------------------------------------------
1 | 1 -2 4 -8 16 -32 64 -128 256 -512 ...
2 | 1 -1 0 1 -1 0 1 -1 0 1 ...
3 | 1 -1 1 -2 3 -4 6 -9 13 -19 ...
4 | 1 -1 1 -1 0 1 -2 3 -3 2 ...
5 | 1 -1 1 -1 1 -2 3 -4 5 -6 ...
6 | 1 -1 1 -1 1 -1 0 1 -2 3 ...
7 | 1 -1 1 -1 1 -1 1 -2 3 -4 ...
8 | 1 -1 1 -1 1 -1 1 -1 0 1 ...
9 | 1 -1 1 -1 1 -1 1 -1 1 -2 ...
10 | 1 -1 1 -1 1 -1 1 -1 1 -1 ...
...
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MATHEMATICA
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f[t_, n_] = 1/(t^n + t + 1);
a = Table[Table[SeriesCoefficient[Series[f[t, m], {t, 0, 30}], n], {n, 0, 30}], {m, 1, 31}];
Flatten[Table[Table[a[[n - m + 1]][[m]], {m, 1, n }], {n, 1, 15}]]
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PROG
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(Maxima) (nn : 12, kk : 50)$
gf(n) := taylor(1/(x^n + x + 1), x, 0, kk)$
T(n, k) := ratcoef(gf(n), x, k)$
create_list(T(n - k, k), n, 1, nn, k, 0, n - 1);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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