A144383 T(n,k) = [t^k] 1/(t^n + t + 1), square array read by ascending antidiagonals (n >= 1, k >= 0).

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

Offset

1,3

Links

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

Example

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 ...
   ...

Mathematica

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}]]

Prog

(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);
/* Franck Maminirina Ramaharo, Jan 18 2019 */

Crossrefs

Cf. A144382, A144384.

Sequence in context: A106246 A340660 A136674 * A205553 A178411 A257598

Adjacent sequences: A144380 A144381 A144382 * A144384 A144385 A144386

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