A144382 T(1,k) = -1 and T(n,k) = [t^k] 1/(-1 + t - t^n) for n >= 2, square array read by ascending antidiagonals (n >= 1, k >= 0).

-1, -1, -1, -1, -1, -1, -1, -1, 0, -1, -1, -1, -1, 1, -1, -1, -1, -1, 0, 1, -1, -1, -1, -1, -1, 1, 0, -1, -1, -1, -1, -1, 0, 2, -1, -1, -1, -1, -1, -1, -1, 1, 2, -1, -1, -1, -1, -1, -1, -1, 0, 2, 1, 0, -1, -1, -1, -1, -1, -1, -1, 1, 3, -1, 1, -1, -1, -1, -1, -1, -1, -1, 0, 2, 3, -3, 1, -1

Offset

1,34

Links

Table of n, a(n) for n=1..78.

Example

Array begins:
  n\k |  0  1  2  3  4  5  6  7  8  9 10 ...
  -------------------------------------------
    1 | -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 ...
    2 | -1 -1  0  1  1  0 -1 -1  0  1  1 ...
    3 | -1 -1 -1  0  1  2  2  1 -1 -3 -4 ...
    4 | -1 -1 -1 -1  0  1  2  3  3  2  0 ...
    5 | -1 -1 -1 -1 -1  0  1  2  3  4  4 ...
    6 | -1 -1 -1 -1 -1 -1  0  1  2  3  4 ...
    7 | -1 -1 -1 -1 -1 -1 -1  0  1  2  3 ...
    8 | -1 -1 -1 -1 -1 -1 -1 -1  0  1  2 ...
    9 | -1 -1 -1 -1 -1 -1 -1 -1 -1  0  1 ...
   10 | -1 -1 -1 -1 -1 -1 -1 -1 -1 -1  0 ...
   ...

Mathematica

f[t_, n_] = If[n == 1, 1/(-1 + t), 1/(-1 + t - t^n)];
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}]]

Prog

(Maxima)(nn : 15, kk : 50)$
gf(n) := taylor(if n = 1 then 1/(1 - x) else  1/(-1 + x - x^n), x, 0, kk)$
T(n, k) := ratcoef(gf(n), x, k)$
create_list(T(n - k, k), n, 1, nn, k, 0, n - 1);
/* Franck Maminirina Ramaharo, Jan 21 2019 */

Crossrefs

Cf. A144383, A144384.

Sequence in context: A037832 A170977 A039737 * A139553 A078379 A121657

Adjacent sequences: A144379 A144380 A144381 * A144383 A144384 A144385

Keyword

sign,easy,tabl

Author

Roger L. Bagula and Gary W. Adamson, Oct 01 2008

Extensions

Edited by Franck Maminirina Ramaharo, Jan 21 2019

Status

approved