cp's OEIS Frontend

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

%I A252745 #8 Jan 04 2015 22:56:21
%S A252745 0,0,1,3,6,15,26,57,118,237,486,989,1992,3997,8038,16133,32331,64777,
%T A252745 129810,260191,521325,1043924,2089305,4180716
%N A252745 Number of ones on each row of irregular tables A252743 and A252744.
%C A252745 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.
%C A252745 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 A252745 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).
%F A252745 Other identities. For n >= 1:
%F A252745 a(n) = 2^(n-1) - A252746(n).
%o A252745 (PARI)
%o A252745 allocatemem(234567890);
%o A252745 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 A252745 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)); };
%o A252745 A252745print(23); \\ The terms a(0) .. a(23) were computed with this program.
%o A252745 (Scheme)
%o A252745 (define (A252745 n) (if (zero? n) 0 (add A252744 (A000079 (- n 1)) (A000225 n))))
%o A252745 (define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))
%Y A252745 Cf. A000079, A000225, A252737, A252743, A252744, A252746.
%K A252745 nonn
%O A252745 0,4
%A A252745 _Antti Karttunen_, Dec 21 2014