1,6

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

Nicholas Hillier, Table of n, a(n) for n = 1..16384

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)

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

(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

Cf. A053644.

Sequence in context: A026515 A075772 A142157 * A375849 A364633 A333513

Adjacent sequences: A119605 A119606 A119607 * A119609 A119610 A119611

easy,nonn,frac

Leroy Quet, Jun 04 2006

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

approved