Search: id:A035507
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%I A035507
%S A035507 1,2,4,3,7,12,5,9,20,33,6,14,25,54,88,8,17,38,67,143,232,10,22,46,101,
%T A035507 177,376,609,11,27,59,122,266,465,986,1596,13,30,72,156,321,698,1219,
%U A035507 2583,4180,15,35,80,190,410,842,1829,3193,6764,10945,16,41,93,211,499
%N A035507 Inverse Stolarsky array read by antidiagonals.
%D A035507 C. Kimberling, "Interspersions and dispersions," Proceedings of the American 
               Mathematical Society 117 (1993) 313-321.
%H A035507 C. Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">
               Interspersions</a>
%H A035507 N. J. A. Sloane, <a href="classic.html#WYTH">Classic Sequences</a>
%F A035507 The term in row n and column k of the inverse Stolarsky array has the 
               following expression: a(n, k)= F(2k-3)-1-c1(n)F(2k-4)+c2(n)F(2k-2), 
               where F is the Fibonacci sequence; c1(n)=1 if n=1, [(n-1)*tau] if 
               n>1 (first column of the Inverse Stolarsky array) and c2(n)=c1(n)+1+floor((2*c1(n)+1)*tau/
               2) (second column of the Inverse Stolarsky array). tau=(1+sqrt(5))/
               2 and [] denotes the nearest integer function. - C. Ronaldo (aga_new_ac(AT)hotmail.com), 
               Dec 31 2004
%F A035507 Also, the following recurrence holds: a(n, k)=3*a(n, k-1)-a(n, k-2)+1 
               with a(n, 1)=c1(n) and a(n, 2)=c2(n). - C. Ronaldo (aga_new_ac(AT)hotmail.com), 
               Dec 31 2004
%e A035507 Top left hand corner of array:
%e A035507 1 4 12 33 88 232...
%e A035507 2 7 20 54 143 376...
%e A035507 3 9 25 67 177 465...
%e A035507 5 14 38 101 266 698...
%p A035507 with(combinat, fibonacci): gold:=(1+sqrt(5))/2: c1:=n->piecewise(n<>1,
               round((n-1)*gold),1): c2:=n->c1(n)+floor((2*c1(n)+1)*gold/2)+1: inv_stol:=(n,
               k)->fibonacci(2*k-3)-1-c1(n)*fibonacci(2*k-4)+c2(n)*fibonacci(2*k-2): 
               seq(seq(inv_stol(n+1-k,k),k=1..n),n=1..11); inv_stol2:=(n,k)->(1+c0(n))*fibonacci(2*k-3)+(1+floor((2*c0(n\
               )+1)*gold/2))*fibonacci(2*k-2)-1:seq(seq(inv_stol2(n+1-k,k),k=1..n),
               n=1..11); (Ronaldo)
%Y A035507 Cf. A035506.
%Y A035507 Sequence in context: A101267 A090568 A166017 this_sequence A138612 A058330 
               A124256
%Y A035507 Adjacent sequences: A035504 A035505 A035506 this_sequence A035508 A035509 
               A035510
%K A035507 nonn,tabl,easy,nice
%O A035507 0,2
%A A035507 N. J. A. Sloane (njas(AT)research.att.com).
%E A035507 More terms from C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 31 2004

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