cp's OEIS Frontend

A252746 Number of zeros on each row of irregular tables A252743 and A252744.

%I A252746 #7 Jan 04 2015 22:56:32
%S A252746 1,1,1,1,2,1,6,7,10,19,26,35,56,99,154,251,437,759,1262,1953,2963,
%T A252746 4652,7847,13588
%N A252746 Number of zeros on each row of irregular tables A252743 and A252744.
%C A252746 Also, number of nodes on level n (the root 1 occurs at level 0) of binary tree depicted in A005940 where the left hand child is less than the right hand child of the node.
%C A252746 E.g. on the level 2, containing nodes 3 and 4, the children of 3 are 5 < 6, and the children of 4 are 9 > 8, thus a(2) = 1.
%F A252746 a(n) = 2^(n-1) - A252745(n).
%o A252746 (PARI)
%o A252746 allocatemem(234567890);
%o A252746 A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ Using code of _Michel Marcus_
%o A252746 A252746print(up_to_n) = { my(s, i=0, n=0); for(n=0, up_to_n, if(0 == n, s = 1; lev = vector(1); lev[1] = 2, oldlev = lev; lev = vector(2*length(oldlev)); s = 0; for(i = 0, (2^n)-1, lev[i+1] = if(!(i%2),A003961(oldlev[(i\2)+1]),2*oldlev[(i\2)+1]); s += if((i%2),(lev[i+1] > lev[i]),0))); write("b252746.txt", n, " ", s)); };
%o A252746 A252746print(23); \\ The terms a(0) .. a(23) were computed with this program.
%o A252746 (Scheme) (define (A252746 n) (if (= 0 n) 1 (- (A000079 (- n 1)) (A252745 n))))
%Y A252746 Cf. A000079, A000225, A252737, A252743, A252744, A252745.
%K A252746 nonn,more
%O A252746 0,5
%A A252746 _Antti Karttunen_, Dec 21 2014