A163253 An interspersion: the order array of the odd-numbered columns of the double interspersion at A161179.

1, 4, 2, 9, 5, 3, 16, 10, 7, 6, 25, 17, 13, 11, 8, 36, 26, 21, 18, 14, 12, 49, 37, 31, 27, 22, 19, 15, 64, 50, 43, 38, 32, 28, 23, 20, 81, 65, 57, 51, 44, 39, 33, 29, 24, 100, 82, 73, 66, 58, 52, 45, 40, 34, 30, 121, 101, 91, 83, 74, 67, 59, 53, 46, 41, 35

Offset

1,2

Comments

A permutation of the natural numbers.

Row 1 consists of the squares.

Beginning with row 5, the columns obey a 3rd-order recurrence:

c(n)=c(n-1)+c(n-2)-c(n-3)+1; thus disregarding row 1, the nonsquares are partitioned by this recurrence.

Except for initial terms, the first ten rows match A000290, A002522, A002061, A059100, A014209, A117950, A027688, A087475, A027689, A117951, and the first column, A035106.

Links

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

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. Three cases:

S(1,k)=k^2;

if n is even, then S(n,k)=k^2+(n-2)k+(n^2-2*n+4)/4;

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

Example

Corner:
1....4....9...16...25
2....5...10...17...26
3....7...13...21...31
6...11...18...27...38
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 even-numbered columns, leaving
1....7...17...
2....8...18...
5...13...25...
9...19...33...
Then replace each of those numbers by its rank when all the numbers are jointly ranked.

Crossrefs

Cf. A000037, A000290, A161179, A163254, A163255, A163256, A163257, A163258.

Sequence in context: A194032 A191739 A091450 * A191663 A206561 A008831

Adjacent sequences: A163250 A163251 A163252 * A163254 A163255 A163256

Keyword

nonn,tabl

Author

Clark Kimberling, Jul 23 2009

Extensions

Edited and augmented by Clark Kimberling, Jul 24 2009

Status

approved