A252745 Number of ones on each row of irregular tables A252743 and A252744.

0, 0, 1, 3, 6, 15, 26, 57, 118, 237, 486, 989, 1992, 3997, 8038, 16133, 32331, 64777, 129810, 260191, 521325, 1043924, 2089305, 4180716

Offset

0,4

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 larger 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(0) = 1; for n>1: a(n) = Sum_{k=A000079(n-1) .. A000225(n)} A252743(k) = Sum_{k=2^(n-1) .. (2^n)-1} A252744(k).

Other identities. For n >= 1:

a(n) = 2^(n-1) - A252746(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
A252745print(up_to_n) = { my(s, i=0, n=0); for(n=0, up_to_n, if(0 == n, s = 0; 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("b252745.txt", n, " ", s)); };
A252745print(23); \\ The terms a(0) .. a(23) were computed with this program.
(Scheme)
(define (A252745 n) (if (zero? n) 0 (add A252744 (A000079 (- n 1)) (A000225 n))))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))

Crossrefs

Cf. A000079, A000225, A252737, A252743, A252744, A252746.

Sequence in context: A079825 A339394 A327067 * A282662 A282123 A281420

Adjacent sequences: A252742 A252743 A252744 * A252746 A252747 A252748

Keyword

nonn

Author

Antti Karttunen, Dec 21 2014

Status

approved