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A137707 Secondary Wythoff Array read by antidiagonals. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 A266794

Adjacent sequences:  A137704 A137705 A137706 * A137708 A137709 A137710

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Feb 07 2008

STATUS

approved

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Last modified December 5 07:41 EST 2016. Contains 278761 sequences.