A120405 - OEIS

%I #15 Feb 13 2022 23:21:15

%S 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,

%T 168,315,1024,1,2,3,8,5,12,21,64,9,20,33,96,65,168,315,1024,17,36,57,

%U 160,105,264,483,1536,225,520,891,2688,1885,5040,9765,32768,1,2,3,8,5

%N 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.

%H Harvey P. Dale, <a href="/A120405/b120405.txt">Table of n, a(n) for n = 1..10000</a>

%F 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.

%F a(2^k+m) = m*a(m), 1 <= m < 2^k, k=0,1,2,3,... - _R. J. Mathar_, Aug 17 2006

%p 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

%t Nest[Join[#,# Range[Length[#]]]&,{1,1},6] (* _Harvey P. Dale_, Nov 23 2014 *)

%Y Cf. A120768 (partial sums).

%K nonn

%O 1,4

%A _Gary W. Adamson_, Jul 03 2006

%E More terms from _R. J. Mathar_, Aug 17 2006