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

1, 1, 1, 1, 2, 1, 6, 7, 10, 19, 26, 35, 56, 99, 154, 251, 437, 759, 1262, 1953, 2963, 4652, 7847, 13588

Offset

0,5

Comments

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.

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.

Links

Table of n, a(n) for n=0..23.

Formula

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

Prog

(PARI)
allocatemem(234567890);
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
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)); };
A252746print(23); \\ The terms a(0) .. a(23) were computed with this program.
(Scheme) (define (A252746 n) (if (= 0 n) 1 (- (A000079 (- n 1)) (A252745 n))))

Crossrefs

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

Sequence in context: A160348 A047708 A256277 * A182883 A172285 A192232

Adjacent sequences: A252743 A252744 A252745 * A252747 A252748 A252749

Keyword

nonn,more

Author

Antti Karttunen, Dec 21 2014

Status

approved