A163257 An interspersion: the order array of the even-numbered columns (after swapping the first two rows) of the double interspersion at A161179.

1, 5, 2, 11, 6, 3, 19, 12, 8, 4, 29, 20, 15, 10, 7, 41, 30, 24, 18, 14, 9, 55, 42, 35, 28, 23, 17, 13, 71, 56, 48, 40, 34, 27, 22, 16, 89, 72, 63, 54, 47, 39, 33, 26, 21, 109, 90, 80, 70, 62, 53, 46, 38, 32, 25, 131, 110, 99, 88, 79, 69, 61, 52, 45, 37, 31, 155, 132, 120, 108

Offset

1,2

Comments

A permutation of the natural numbers.

Beginning at row 6, the columns obey a 3rd-order recurrence:

c(n)=c(n-1)+c(n-2)-c(n-3)+1.

Except for initial terms, the first seven rows are A028387, A002378, A005563, A028552, A008865, A014209, A028873, and the first column, A004652.

Links

Table of n, a(n) for n=1..70.

Clark Kimberling, Doubly interspersed sequences, double interspersions and fractal sequences, The Fibonacci Quarterly 48 (2010) 13-20.

Formula

Let S(n,k) denote the k-th term in the n-th row. Four cases:

S(1,k)=k^2+k-1

S(2,k)=k^2+k

if n>1 is odd, then S(n,k)=k^2+(n-1)k+(n-1)(n-3)/4

if n>2 is even, then S(n,k)= k^2+(n-1)k+n(n-4)/4.

Example

Corner:
1....5...11...19
2....6...12...20
3....8...15...24
4...10...18...28
The double interspersion A161179 begins thus:
1....4....7...12...17...24
2....3....8...11...18...23
5....6...13...16...25...30
9...10...19...22...33...38
Expel the odd-numbered columns and then swap rows 1 and 2, leaving
3....11...23...39
4....12...24...40
6....16...30...48
10...22...38...58
Then replace each of those numbers by its rank when all the numbers are jointly ranked.

Crossrefs

Cf. A163253, A163254, A163255, A163256, A163258.

Sequence in context: A257327 A074642 A194034 * A332452 A176624 A131784

Adjacent sequences: A163254 A163255 A163256 * A163258 A163259 A163260

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 24 2009

Status

approved