A119608 Let b(1)=0, b(2)= 1. b(2^m +k) = (b(2^m+1-k) + b(k))/2, 1 <= k <= 2^m, m >= 0. a(n) is numerator of b(n).

0, 1, 1, 1, 1, 3, 3, 1, 1, 7, 5, 3, 3, 5, 7, 1, 1, 15, 9, 7, 5, 11, 13, 3, 3, 13, 11, 5, 7, 9, 15, 1, 1, 31, 17, 15, 9, 23, 25, 7, 5, 27, 21, 11, 13, 19, 29, 3, 3, 29, 19, 13, 11, 21, 27, 5, 7, 25, 23, 9, 15, 17, 31, 1, 1, 63, 33, 31, 17, 47, 49, 15, 9, 55, 41, 23, 25, 39, 57, 7, 5, 59, 37

Offset

1,6

Comments

Denominator of b(n), for n >= 2, is A053644(n-1).

Links

Table of n, a(n) for n=1..83.

Formula

From Yosu Yurramendi, Mar 13 2019: (Start)

Without a(1) = 0, and shifting the terms one place left:

a(2^m) = 1, m >= 0;

a(2^(m+1)-1-k) = a(2^m+k), m >= 0, 0 < k < 2^m;

a(2^(m+1)+k) = a(2^m+k)+2^(m-floor(log_2(k)))*a(k), m >= 0, 0 < k < 2^m.

(End)

Maple

A119608 := proc (mmax) local a, b, m, k, bn, i; b := [0, 1] ; for m from 1 to mmax do for k from 1 to 2^m do bn := (b[2^m+1-k]+b[k])/2 ; b := [op(b), bn] ; od ; od ; a := [] ; for i from 1 to nops(b) do a := [op(a), numer(b[i])] ; od ; RETURN(a) ; end: an := A119608(7) : for i from 1 to nops(an) do printf("%d, ", an[i]) ; od ; # R. J. Mathar, Aug 06 2006

Prog

(R)
maxlevel <- 8 # by choice
b <- c(0, 1)
for(m in 1:maxlevel) for(k in 1:2^m) b[2^m +k] = (b[2^m+1-k] + b[k])/2
d <- vector()
for(m in 0:maxlevel) for(k in 0:(2^m-1)) d[2^m + k] <- 2^m; d <- c(0, d)
a <- b*d
a[1:100]
# Yosu Yurramendi, Feb 05 2019
(R)
a <- 1
maxlevel <- 15 # by choice
for(m in 1:5) {
  a[2^(m+1)-1] <- 1
  a[2^(m+1)  ] <- 1
  for(k in 1:(2^m-1)){
  a[2^(m+1)-1-k] <- a[2^m+k]
  a[2^(m+1)  +k] <- a[2^m+k]+2^(m-floor(log2(k)))*a[k]
}}
a <- c(0, a)
a[1:128]
# Yosu Yurramendi, Mar 13 2019

Crossrefs

Cf. A053644.

Sequence in context: A026515 A075772 A142157 * A364633 A333513 A196646

Adjacent sequences: A119605 A119606 A119607 * A119609 A119610 A119611

Keyword

easy,nonn,frac

Author

Leroy Quet, Jun 04 2006

Extensions

More terms from R. J. Mathar, Aug 06 2006

Status

approved