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A245547
Write n>=1 as either n=2^k-2^r with 0 <= r <= k-1, in which case a(2^k-2^r)=(k-r)*(k-r+1)/2, or as n=2^k-2^r+j with 2 <= r <= k-1, 1 <= j < 2^r-1, in which case a(2^k-2^r+j)=(k-r)*(k-r+1)*a(j).
2
1, 1, 3, 1, 2, 3, 6, 1, 2, 2, 6, 3, 6, 6, 10, 1, 2, 2, 6, 2, 4, 6, 12, 3, 6, 6, 18, 6, 12, 10, 15, 1, 2, 2, 6, 2, 4, 6, 12, 2, 4, 4, 12, 6, 12, 12, 20, 3, 6, 6, 18, 6, 12, 18, 36, 6, 12, 12, 36, 10, 20, 15, 21, 1, 2, 2, 6, 2, 4, 6, 12, 2, 4, 4, 12, 6, 12, 12, 20, 2, 4, 4, 12, 4, 8, 12, 24, 6
OFFSET
1,3
COMMENTS
See A245196 for a list of other sequences produced by this type of recurrence.
It follows from the definition that the final entries in the blocks are triangular numbers.
EXAMPLE
Arranged into blocks:
1,
1, 3,
1, 2, 3, 6,
1, 2, 2, 6, 3, 6, 6, 10,
1, 2, 2, 6, 2, 4, 6, 12, 3, 6, 6, 18, 6, 12, 10, 15,
1, 2, 2, 6, 2, 4, 6, 12, 2, 4, 4, 12, 6, 12, 12, 20, 3, 6, 6, 18, 6, 12, 18, 36, 6, 12, 12, 36, 10, 20, 15, 21,
...
MAPLE
G:=[seq(n, n=0..30)];
m:=2;
f:=proc(n) option remember; global m, G; local k, r, j, np;
k:=1+floor(log[2](n)); np:=2^k-n;
if np=1 then r:=0; j:=0; else r:=1+floor(log[2](np-1)); j:=2^r-np; fi;
if j=0 then G[k-r]; else m*G[k-r]*f(j); fi;
end;
[seq(f(n), n=1..120)];
CROSSREFS
Sequence in context: A165520 A107341 A209849 * A138881 A070983 A078350
KEYWORD
nonn,tabf
AUTHOR
N. J. A. Sloane, Jul 27 2014
STATUS
approved