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A120405
a(n) = 1, a(2) = 1, then append the dot product of (1,2) and (1,1) = 1*1, 1*2 = 1, 2; to the right of 1, 1; getting (1, 1, 1, 2). The next operation uses the dot product of (1, 2, 3, 4) and (1, 1, 1, 2), getting (1, 2, 3, 8) which we append to the right of (1, 1, 1, 2), getting (1, 1, 1, 2, 1, 2, 3, 8) and so on.
4
1, 1, 1, 2, 1, 2, 3, 8, 1, 2, 3, 8, 5, 12, 21, 64, 1, 2, 3, 8, 5, 12, 21, 64, 9, 20, 33, 96, 65, 168, 315, 1024, 1, 2, 3, 8, 5, 12, 21, 64, 9, 20, 33, 96, 65, 168, 315, 1024, 17, 36, 57, 160, 105, 264, 483, 1536, 225, 520, 891, 2688, 1885, 5040, 9765, 32768, 1, 2, 3, 8, 5
OFFSET
1,4
LINKS
FORMULA
Given a(1) = 1, perform the operation n * a(n) and append to the right of current subset; each operation doubles the number of terms.
a(2^k+m) = m*a(m), 1 <= m < 2^k, k=0,1,2,3,... - R. J. Mathar, Aug 17 2006
MAPLE
A120405 := proc(n) local l, bas ; if n = 1 then RETURN(1) ; else bas := floor( log[2](n-1) ) ; l := n-2^bas ; RETURN(l*A120405(l)) ; fi ; end; for n from 1 to 200 do printf("%d, ", A120405(n)) ; od ; # R. J. Mathar, Aug 17 2006
MATHEMATICA
Nest[Join[#, # Range[Length[#]]]&, {1, 1}, 6] (* Harvey P. Dale, Nov 23 2014 *)
CROSSREFS
Cf. A120768 (partial sums).
Sequence in context: A051850 A077013 A086880 * A252889 A155004 A176954
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jul 03 2006
EXTENSIONS
More terms from R. J. Mathar, Aug 17 2006
STATUS
approved