|
Search: id:A050447
|
|
|
| A050447 |
|
Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials in m variables, -1 <= n, 1 <= m, transposed and read by antidiagonals. |
|
+0
12
|
|
| 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 5, 1, 1, 5, 10, 14, 8, 1, 1, 6, 15, 30, 31, 13, 1, 1, 7, 21, 55, 85, 70, 21, 1, 1, 8, 28, 91, 190, 246, 157, 34, 1, 1, 9, 36, 140, 371, 671, 707, 353, 55, 1, 1, 10, 45, 204, 658, 1547, 2353, 2037, 793, 89, 1, 1, 11, 55, 285, 1086, 3164
(list; table; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
REFERENCES
|
J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see p. 120).
Manfred Goebel, Rewriting Techniques and Degree Bounds for Higher Order Symmetric Polynomials, Applicable Algebra in Engineering, Communication and Computing (AAECC), Volume 9, Issue 6 (1999), 559-573.
G. Kreweras, Les preordres totaux compatibles avec un ordre partiel. Math. Sci. Humaines No. 53 (1976), 5-30.
|
|
FORMULA
|
See PARI code. See A050446 for recurrence.
|
|
EXAMPLE
|
Table begins
1 1 1 1 1 1 1 ...
1 2 3 4 5 6 7 ...
1 3 6 10 15 21 28 ...
1 5 14 30 55 91 140 ...
1 8 31 85 190 371 658 ...
|
|
PROGRAM
|
(PARI) M(n)=matrix(n, n, i, j, if(sign(i+j-n)-1, 0, 1)); V(n)=vector(n, i, 1); P(r, n)=vecmax(V(r)*M(r)^n) (from Benoit Cloitre, Jan 27, 2003. P(r, n) is T(n, k).)
|
|
CROSSREFS
|
Rows give A000217, A000330, A006322, ..., columns give A000045, A006356, A006357, A006358, ... Cf. A050446.
Adjacent sequences: A050444 A050445 A050446 this_sequence A050448 A050449 A050450
Sequence in context: A073714 A144151 A022818 this_sequence A166293 A094525 A130671
|
|
KEYWORD
|
nonn,easy,nice,tabl
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999
|
|
EXTENSIONS
|
More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 03 2001
|
|
|
Search completed in 0.002 seconds
|
