1,2

(Row 2) is possibly A074323 except for an initial 1. The sequence represents the para-sequence in which the "final ordering" << is given by 1 << ... << 4 << 3 << 2. Row n contains 1,2,3,...2n, but not 2n+1. Row n starts like row n of A134625; e.g., row 6 of A123625 and row of A134626 have the same first 16 terms.

C. Kimberling, Proper self-containing sequences, fractal sequences, and para-sequences, preprint, 2007.

Row 1 is A000079. Row n>=2 is produced from row n by the sum-fill operation, defined on an arbitrary infinite or finite sequence x = (x(1), x(2), x(3), ...) by the following two steps: Step 1. Form the sequence x(1), x(1)+x(2), x(2), x(2)+x(3), x(3), x(3)+x(4), ...; i.e., fill the space between x(n) and x(n+1) by their sum. Step 2. Delete duplicates; i.e., letting y be the sequence resulting from Step 1, if y(n+h)=y(n) for some h>=1, then delete y(n+h).

Starting with x = row 3, Step 1 gives

y = (1,5,4,7,3,8,5,7,2,10,8,14,6,...).

Delete the second 5,7,8,... leaving row 4:

(1,5,4,7,3,8,2,10,14,6,...).

Northwest corner:

1 2 4 8 16 32

1 3 2 6 4 12

1 4 3 5 2 8

1 5 4 7 3 8

1 6 5 9 4 11.

Cf. A134625, A134627, A134628.

Adjacent sequences: A134623 A134624 A134625 this_sequence A134627 A134628 A134629

Sequence in context: A131252 A133805 A131254 this_sequence A115450 A109435 A134392

nonn,tabl

Clark Kimberling (ck6(AT)evansville.edu), Nov 04 2007