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Number of zeros on each row of irregular tables A252743 and A252744.
5

%I #7 Jan 04 2015 22:56:32

%S 1,1,1,1,2,1,6,7,10,19,26,35,56,99,154,251,437,759,1262,1953,2963,

%T 4652,7847,13588

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

%C 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 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 a(n) = 2^(n-1) - A252745(n).

%o (PARI)

%o allocatemem(234567890);

%o 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 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 A252746print(23); \\ The terms a(0) .. a(23) were computed with this program.

%o (Scheme) (define (A252746 n) (if (= 0 n) 1 (- (A000079 (- n 1)) (A252745 n))))

%Y Cf. A000079, A000225, A252737, A252743, A252744, A252745.

%K nonn,more

%O 0,5

%A _Antti Karttunen_, Dec 21 2014