login
Wythoff array read by antidiagonals.
5

%I #15 Feb 10 2021 02:02:45

%S 1,4,2,6,7,3,9,10,11,5,12,15,16,18,8,14,20,24,26,29,13,17,23,32,39,42,

%T 47,21,19,28,37,52,63,68,76,34,22,31,45,60,84,102,110,123,55,25,36,50,

%U 73,97,136,165,178,199,89,27,41,58,81,118,157,220,267,288,322,144,30,44

%N Wythoff array read by antidiagonals.

%C The first term in each row is the least summand in the Zeckendorf representation of every term in the row. - _Clark Kimberling_, Aug 27 2008

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/WythoffArray.html">Wythoff Array</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%p W:= proc(n,k) Digits:= 100; (Matrix([n, floor((1+sqrt(5))/2* (n+1))]). Matrix([[0,1], [1,1]])^(k+1))[1,2] end: seq(seq(W(d-k, k), k=0..d), d=0..10); # _Alois P. Heinz_, Aug 18 2008

%t W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k]; t = Table[ W[n - k + 1, k], {n, 12}, {k, n}] // Flatten

%Y A035513 transposed. See that entry for further details.

%K nonn,tabl

%O 0,2

%A _N. J. A. Sloane_, Jun 09 2003

%E More terms from _Alois P. Heinz_, Aug 18 2008