_Clark Kimberling (ck6(AT)evansville.edu), _, Feb 07 2008

(1) Delete the odd numbered rows and get twice the Wythoff array, A035513. (2) Subtract 1 from the even numbered rows and get the odd numbered rows. (3) As a sequence, this is a permutation of the positive integers. (4) The array is a dispersion and an interspersion. (5) Let c = ordered union of odd numbered columns, and let d = ordered union of even numbered columns; then c and d are the unique solutions of the complementary equation d(n)=c(c(n))+2 and also of the complementary equation d(n)=c(n)+2*Floor[(n+2)/2]. (6) c=A137708, d=A137709.

nonn,tabl,new

Secondary Wythoff Array read by antidiagonals.

1, 3, 2, 5, 4, 7, 9, 6, 13, 8, 15, 10, 21, 14, 11, 25, 16, 35, 22, 19, 12, 41, 26, 57, 36, 31, 20, 17, 67, 42, 93, 58, 51, 32, 29, 18, 109, 68, 151, 94, 83, 52, 47, 30, 23, 177, 110, 245, 152, 135, 84, 77, 48, 39, 24, 286, 178, 397, 246, 220, 136, 125, 78, 63, 40, 27

1,2

(1) Delete the odd numbered rows and get twice the Wythoff array, A035513. (2) Subtract 1 from the even numbered rows and get the odd numbered rows. (3) As a sequence, this is a permutation of the positive integers. (4) The array is a dispersion and an interspersion. (5) Let c = ordered union of odd numbered columns, and let d = ordered union of even numbered columns; then c and d are the unique solutions of the complementary equation d(n)=c(c(n))+2 and also of the complementary equation d(n)=c(n)+2*Floor[(n+2)/2]. (6) c=A137708, d=A137709.

Odd numbered rows: r(n)=r(n-1)+r(n-2)+1, Even numbered rows: r(n)=r(n-1)+r(n-2).

Northwest corner:

1 3 5 9 15

2 4 6 10 16

7 13 21 35 57

8 14 22 36 58

Cf. A035513, A137708, A137709.

nonn,tabl

Clark Kimberling (ck6(AT)evansville.edu), Feb 07 2008

approved