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.

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

Harvey P. Dale, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A120402 A120403 A120404 * A120406 A120407 A120408

Keyword

nonn

Author

Gary W. Adamson, Jul 03 2006

Extensions

More terms from R. J. Mathar, Aug 17 2006

Status

approved