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

Author

Antti Karttunen, Dec 21 2014

Keywords

• nonn

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.

Crossrefs

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

Programs

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)))))))

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).