|
| |
|
|
A163257
|
|
An interspersion: the order array of the even-numbered columns (after swapping the first two rows) of the double interspersion at A161179.
|
|
4
| |
|
|
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
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
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.
|
|
|
REFERENCES
| 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
| A163253, A163254, A163255, A163256, A163258.
Sequence in context: A051308 A074642 A194034 * A176624 A131784 A065268
Adjacent sequences: A163254 A163255 A163256 * A163258 A163259 A163260
|
|
|
KEYWORD
| nonn,tabl
|
|
|
AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jul 24 2009
|
| |
|
|
