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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..59.

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=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 is:

1 3 8 21 55 144 ...

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. Cf. A035506.

Sequence in context: A277905 A257802 A225850 * A182831 A257725 A257690

Adjacent sequences:  A038147 A038148 A038149 * A038151 A038152 A038153

KEYWORD

nonn,tabl,nice,easy

AUTHOR

Aviezri S. Fraenkel

EXTENSIONS

More terms from Naohiro Nomoto, Jun 07 2001

STATUS

approved

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Last modified September 15 08:13 EDT 2019. Contains 327062 sequences. (Running on oeis4.)