OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..16384 (first 1024 terms from Paul D. Hanna)
FORMULA
a(2^n)=2^n.
a(2*n-1)=a(n), a(2*n)=n+a(n).
EXAMPLE
A088370 rows: {1}, {1, 2}, {1, 3, 2}, {1, 3, 2, 4}, {1, 5, 3, 2, 4}, {1, 5, 3, 2, 6, 4}, {1, 5, 3, 7, 2, 6, 4}, ...
Row 5 is formed from row 3, {1, 3, 2} and row 2, {1, 2}: {1, 5, 3, 2, 4} = {1*2-1, 3*2-1, 2*2-1}|{1*2, 2*2}.
This sequence can form the following irregular triangle:
1;
2;
2, 4;
2, 5, 4, 8;
2, 7, 5, 11, 4, 11, 8, 16;
2, 11, 7, 17, 5, 16, 11, 23, 4, 17, 11, 25, 8, 23, 16, 32;
2, 19, 11, 29, 7, 26, 17, 37, 5, 26, 16, 38, 11, 34, 23, 47, 4, 29, 17, 43, 11, 38, 25, 53, 8, 37, 23, 53, 16, 47, 32, 64;
2, 35, 19, 53, 11, 46, 29, 65, 7, 44, 26, 64, 17, 56, 37, 77, 5, 46, 26, 68, 16, 59, 38, 82, 11, 56, 34, 80, 23, 70, 47, 95, 4, 53, 29, 79, 17, 68, 43, 95, 11, 64, 38, 92, 25, 80, 53, 109, 8, 65, 37, 95, 23, 82, 53, 113, 16, 77, 47, 109, 32, 95, 64, 128; ...
MAPLE
a:= proc(n) option remember; `if`(n<2, n,
`if`(n::odd, a(n/2+1/2), a(n/2)+n/2))
end:
seq(a(n), n=1..128); # Alois P. Heinz, Jul 26 2019
PROG
(PARI) L=100; b=vector(L, k, k); c=vector(L); a=vector(L, k, b); a[1]=[1]; print1(1, ", "); for(n=2, L, i=floor((n+1)/2); j=floor(n/2); b=a[i]; b=vector(i, k, b[k]=2*b[k]-1 ); c=a[j]; c=vector(j, k, c[k]=2*c[k]); a[n]=concat(b, c); t=a[n]; for(k=1, n, if(t[k]==n, print1(k, ", "); k=n+1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 28 2003
STATUS
approved