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%I #12 Jan 22 2019 08:47:19
%S 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,
%T 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,
%U 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
%N T(n,k) = [t^k] 1/(t^n + t + 1), square array read by ascending antidiagonals (n >= 1, k >= 0).
%e Square array begins:
%e n\k | 0 1 2 3 4 5 6 7 8 9 ...
%e --------------------------------------------
%e 1 | 1 -2 4 -8 16 -32 64 -128 256 -512 ...
%e 2 | 1 -1 0 1 -1 0 1 -1 0 1 ...
%e 3 | 1 -1 1 -2 3 -4 6 -9 13 -19 ...
%e 4 | 1 -1 1 -1 0 1 -2 3 -3 2 ...
%e 5 | 1 -1 1 -1 1 -2 3 -4 5 -6 ...
%e 6 | 1 -1 1 -1 1 -1 0 1 -2 3 ...
%e 7 | 1 -1 1 -1 1 -1 1 -2 3 -4 ...
%e 8 | 1 -1 1 -1 1 -1 1 -1 0 1 ...
%e 9 | 1 -1 1 -1 1 -1 1 -1 1 -2 ...
%e 10 | 1 -1 1 -1 1 -1 1 -1 1 -1 ...
%e ...
%t f[t_, n_] = 1/(t^n + t + 1);
%t a = Table[Table[SeriesCoefficient[Series[f[t, m], {t, 0, 30}], n], {n, 0, 30}], {m, 1, 31}];
%t Flatten[Table[Table[a[[n - m + 1]][[m]], {m, 1, n }], {n, 1, 15}]]
%o (Maxima) (nn : 12, kk : 50)$
%o gf(n) := taylor(1/(x^n + x + 1), x, 0, kk)$
%o T(n, k) := ratcoef(gf(n), x, k)$
%o create_list(T(n - k, k), n, 1, nn, k, 0, n - 1);
%o /* _Franck Maminirina Ramaharo_, Jan 18 2019 */
%Y Cf. A144382, A144384.
%K sign,easy,tabl
%O 1,3
%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 01 2008
%E Edited by _Franck Maminirina Ramaharo_, Jan 21 2019
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