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).

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.

Links

Table of n, a(n) for n=1..88.

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

Cf. A245196, A245541.

Sequence in context: A165520 A107341 A209849 * A138881 A070983 A078350

Adjacent sequences: A245544 A245545 A245546 * A245548 A245549 A245550

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jul 27 2014

Status

approved