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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 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.)