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A245541 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)/2)*a(j). 2
1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 3, 3, 3, 6, 10, 1, 1, 1, 3, 1, 1, 3, 6, 3, 3, 3, 9, 6, 6, 10, 15, 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 3, 3, 3, 6, 10, 3, 3, 3, 9, 3, 3, 9, 18, 6, 6, 6, 18, 10, 10, 15, 21, 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 3, 3, 3, 6, 10, 1, 1, 1, 3, 1, 1, 3, 6, 3, 3, 3, 9, 6, 6, 10, 15 (list; graph; refs; listen; history; text; internal format)
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..95.

EXAMPLE

Arranged into blocks:

1,

1, 3,

1, 1, 3, 6,

1, 1, 1, 3, 3, 3, 6, 10,

1, 1, 1, 3, 1, 1, 3, 6, 3, 3, 3, 9, 6, 6, 10, 15,

1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 3, 3, 3, 6, 10, 3, 3, 3, 9, 3, 3, 9, 18, 6, 6, 6, 18, 10, 10, 15, 21,

...

MAPLE

G:=[seq(n, n=0..30)];

m:=1;

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, A245547.

Sequence in context: A079650 A094644 A113046 * A209563 A308624 A133825

Adjacent sequences:  A245538 A245539 A245540 * A245542 A245543 A245544

KEYWORD

nonn,tabf

AUTHOR

N. J. A. Sloane, Jul 26 2014

STATUS

approved

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Last modified July 22 15:12 EDT 2019. Contains 325224 sequences. (Running on oeis4.)