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

Author

Clark Kimberling, Jul 24 2009

Keywords

• nonn
• tabl

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.

Examples

			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.
		

Links

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

Crossrefs

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

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.