Search: id:A035506
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%I A035506
%S A035506 1,2,4,3,6,7,5,10,11,9,8,16,18,15,12,13,26,29,24,19,14,21,42,47,39,31,
%T A035506 23,17,34,68,76,63,50,37,28,20,55,110,123,102,81,60,45,32,22,89,178,
%U A035506 199,165,131,97,73,52,36,25,144,288,322,267,212,157,118,84,58
%N A035506 Stolarsky array read by antidiagonals.
%C A035506 Inverse of sequence A064357 considered as a permutation of the positive 
               integers. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
%C A035506 GP-PARI program gives general solution for the Stolarsky array in square 
               array form by row,column. Increase the default precision, if computing 
               large values in the array. - Randall L. Rathbun (randallr(AT)abac.com), 
               Jan 25 2002
%D A035506 C. Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 
               129-138.
%D A035506 C. Kimberling, "Interspersions and dispersions," Proceedings of the American 
               Mathematical Society 117 (1993) 313-321.
%H A035506 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">
               Interspersions</a>
%H A035506 N. J. A. Sloane, <a href="classic.html#WYTH">Classic Sequences</a>
%H A035506 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               StolarskyArray.html">Stolarsky arrays</a>
%H A035506 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%e A035506 Top left corner of array is:
%e A035506 1 2 3 5 8 13...
%e A035506 4 6 10 16 26...
%e A035506 7 11 18 29 47...
%e A035506 9 15 24 39 63...
%p A035506 A := proc (n,k) local t,a,b; t:= (1+sqrt(5))/2; a:= floor (n*(1+t)-t/
               2); b:= round (a*t); (Matrix([[b, a]]). Matrix([[1,1], [1,0]])^(k-1))[1,
               2] end: seq (seq (A (n,d-n), n=1..d-1), d=1..11); [From Alois P. 
               Heinz (heinz(AT)hs-heilbronn.de), Aug 17 2008]
%o A035506 (PARI) {Stolarsky(r,c)= tau=(1+sqrt(5))/2; a=floor(r*(1+tau)-tau/2); 
               b=round(a*tau); if(c==1,a, if(c==2,b, for(i=1,c-2,d=a+b; a=b; b=d; 
               ); d))}
%Y A035506 Sequence in context: A083050 A083044 A126714 this_sequence A006016 A054239 
               A048680
%Y A035506 Adjacent sequences: A035503 A035504 A035505 this_sequence A035507 A035508 
               A035509
%K A035506 nonn,tabl,easy,nice
%O A035506 0,2
%A A035506 N. J. A. Sloane (njas(AT)research.att.com).
%E A035506 More terms from Larry Reeves (larryr(AT)acm.org), Sep 27 2000

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