|
Search: id:A038722
|
|
|
| A038722 |
|
Take the sequence of natural numbers (A000027) and reverse successive subsequences of lengths 1,2,3,4,... |
|
+0
7
|
|
| 1, 3, 2, 6, 5, 4, 10, 9, 8, 7, 15, 14, 13, 12, 11, 21, 20, 19, 18, 17, 16, 28, 27, 26, 25, 24, 23, 22, 36, 35, 34, 33, 32, 31, 30, 29, 45, 44, 43, 42, 41, 40, 39, 38, 37, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 78, 77, 76
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
The rectangular array having A038722 as antidiagonals is the transpose of the rectangular array given by A000217. Column 1 of array A038722 is A000124 (central polygonal numbers). Array A038722 is the dispersion of the complement of A000124. - Clark Kimberling (ck6(AT)evansville.edu), Apr 05 2003
|
|
REFERENCES
|
Suggested by correspondence with Michael Somos.
R. Honsberger, "Ingenuity in Mathematics", Table 10.4 on page 87.
|
|
LINKS
|
Index entries for sequences that are permutations of the natural numbers
|
|
FORMULA
|
a(n) =[sqrt(2n-1)-1/2]*[sqrt(2n-1)+3/2]-n+2 =A061579(n-1)+1. Seen as a square table by antidiagonals, T(n, k)=k+(n+k-1)*(n+k-2)/2, i.e. the transpose of A000027 as a square table.
G.f.: g(x)=x/(1-x)*(psi(x)-x/(1-x)+2*sum{k>=0, k*x^(k*(k+1)/2)}) where psi(x)=sum{k>=0, x^(k*(k+1)/2)}=1/2*x^(-1/8)*theta_2(0,x^(1/2) is a Ramanujan theta function. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Aug 08 2007
|
|
CROSSREFS
|
A self-inverse permutation of the natural numbers.
Cf. A000027, A020703.
Sequence in context: A058401 A105027 A120913 this_sequence A131968 A132665 A132667
Adjacent sequences: A038719 A038720 A038721 this_sequence A038723 A038724 A038725
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
njas, May 02 2000
|
|
|
Search completed in 0.002 seconds
|
