login
A038150
Array of numbers used in exotic ternary numeration system, read by antidiagonals.
5
1, 2, 3, 4, 6, 8, 5, 11, 16, 21, 7, 14, 29, 42, 55, 9, 19, 37, 76, 110, 144, 10, 24, 50, 97, 199, 288, 377, 12, 27, 63, 131, 254, 521, 754, 987, 13, 32, 71, 165, 343, 665, 1364, 1974, 2584, 15, 35, 84, 186, 432, 898, 1741, 3571, 5168, 6765, 17, 40, 92, 220, 487
OFFSET
0,2
LINKS
A. S. Fraenkel, Recent results and questions in combinatorial game complexities, Theoretical Computer Science, vol. 249, no. 2 (2000), 265-288.
A. S. Fraenkel, Arrays, numeration systems and Frankenstein games, Theoret. Comput. Sci. 282 (2002), 271-284; preprint.
FORMULA
For n >= 0, A_0^n is the least nonnegative integer not in {A_j^n: 0 <= i < n, j >= 0, A_1^n = 2A_0^n + n, A_j^n = 3A_{j-1}^n - A_{j-2}^n (j >= 2).
a(n,k) = F(2k)*n + F(2k+1)*A026351(n). - Charlie Neder, Feb 07 2019
EXAMPLE
Top left corner of array:
1, 3, 8, 21, 55, ...
2, 6, 16, 42, 110, ...
4, 11, 29, 76, 199, ...
5, 14, 37, 97, 254, ...
MATHEMATICA
t[n_, 1] := Floor[(n - 1) GoldenRatio] + 1; t[n_, j_] := Floor[ GoldenRatio^2 t[n, j - 1]] + 1; Table[ t[n - m + 1, m], {n, 11}, {m, n}] // Flatten (* Birkas Gyorgy, Apr 15 2011; modified by Robert G. Wilson v, Apr 15 2011 *)
CROSSREFS
Rows give A001906, A025169, A002878.
Columns give A026351, A047924, A047925.
Main diagonal gives A047923.
Sequence in context: A257802 A369271 A225850 * A182831 A257725 A257690
KEYWORD
nonn,tabl,nice,easy
EXTENSIONS
More terms from Naohiro Nomoto, Jun 07 2001
STATUS
approved