Search: id:A080164
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%I A080164
%S A080164 1,2,3,5,7,4,13,18,10,6,34,47,26,15,8,89,123,68,39,20,9,233,322,178,102,
%T A080164 52,23,11,610,843,466,267,136,60,28,12,1597,2207,1220,699,356,157,73,31,
%U A080164 14,4181,5778,3194,1830,932,411,191,81,36,16,10946,15127,8362,4791,2440
%N A080164 Wythoff difference array, D={d(i,j)}, by antidiagonals.
%C A080164 D is an interspersion formed by differences between Wythoff pairs in 
               the Wythoff array W={w(i,j)}=A035513 (indexed so that i and j start 
               at 1): d(i,j)=w(i,2j)-w(i,2j-1).
%C A080164 The difference between adjacent column terms is a Fibonacci number: d(i+1,
               j)-d(i,j) is F(2j) or F(2j+1).
%C A080164 Every term in column 1 of W is in column 1 of D and in row i of D, every 
               term except the first is in row i of W.
%C A080164 Let W' be the array remaining when all the odd-numbered columns of W 
               are removed from W. The rank array of W' (obtained by replacing each 
               w'(i,j) by its rank when all the numbers w'(h,k) are arranged in 
               increasing order) is D.
%C A080164 Let W" be the array remaining when all the even-numbered columns of W 
               are removed from W; the rank array of W" is D.
%C A080164 Let D' be the array remaining when column 1 of D is removed; the rank 
               array of D' is D.
%C A080164 Let E be the array {e(i,j)} given by e(i,j)=d(i,2j)-d(i,2j-1); the rank 
               array of E is D.
%D A080164 C. Kimberling, The Wythoff difference array, preprint, 2003.
%D A080164 Clark Kimberling, Complementary Equations, Journal of Integer Sequences, 
               Vol. 10 (2007), Article 07.1.4.
%H A080164 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">
               Interspersions</a>
%H A080164 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%F A080164 d(i, j)=[i*tau]F(2j-1)+(i-1)F(2j-2), where F=A000045 (Fibonacci numbers). 
               d(i, j)=[tau*d(i, j-1)]+d(i, j-1) for i>=2. d(i, j)=3d(i, j-1)-d(i, 
               j-2) for i>=3.
%e A080164 Northwest corner:
%e A080164 1 2 5 13
%e A080164 3 7 18 47
%e A080164 4 10 26 68
%e A080164 6 15 39 102
%e A080164 8 20 52 136
%Y A080164 Cf. A035513, A000201, A001950.
%Y A080164 Sequence in context: A103683 A125151 A103866 this_sequence A126048 A142349 
               A081622
%Y A080164 Adjacent sequences: A080161 A080162 A080163 this_sequence A080165 A080166 
               A080167
%K A080164 nonn,tabl
%O A080164 1,2
%A A080164 Clark Kimberling (ck6(AT)evansville.edu), Feb 08 2003

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