A137707 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

Offset

1,2

Comments

(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.

Links

Table of n, a(n) for n=1..66.

Formula

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

Example

Northwest corner:
1 3 5 9 15
2 4 6 10 16
7 13 21 35 57
8 14 22 36 58

Crossrefs

Cf. A035513, A137708, A137709.

Sequence in context: A191709 A194077 A257334 * A164380 A143527 A284153

Adjacent sequences: A137704 A137705 A137706 * A137708 A137709 A137710

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 07 2008

Status

approved