|
Search: id:A039597
|
|
|
| A039597 |
|
Triangle a(n,k) = number of 2 X inf arrays [ n, n1, n2, ...; k, k1, k2,... ] with n>=n1>n2>...>=0, k>=k1>k2...>=0, n>k, n1>k1, ...; n >= 1, k >= 0. Note that once ni or ki = 0, the strict inequalities become equalities (constant 0 thereafter). |
|
+0
1
|
|
| 2, 4, 6, 8, 14, 20, 16, 30, 50, 70, 32, 62, 112, 182, 252, 64, 126, 238, 420, 672, 924, 128, 254, 492, 912, 1584, 2508, 3432, 256, 510, 1002, 1914, 3498, 6006, 9438, 12870, 512, 1022, 2024, 3938, 7436, 13442, 22880, 35750, 48620, 1024, 2046, 4070, 8008, 15444
(list; table; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
REFERENCES
|
L. Carlitz, Generating functions and partition problems, pp. 144-169 of A. L. Whiteman, ed., Theory of Numbers, Proc. Sympos. Pure Math., 8 (1965). Amer. Math. Soc., see p. 163.
|
|
FORMULA
|
Carlitz gives recurrence.
|
|
EXAMPLE
|
T(2,1) = 6 because the n row can go 2,2,1,0 with the k row either 1,1,0,0 or 1,0,0,0; the n row can go 2,2,0,0 with those same k rows; or the n row can go 2,1,0,0 or 2,0,0,0 with the k row going 1,0,0,0 (since k must be strictly less than n, except when both are 0).
|
|
PROGRAM
|
; ; PLT DrScheme from Joshua Zucker
(define ht (make-hash-table 'equal))
(define (A039597 n k)
(local ((define (help n k)
(cond
[(= n 0) (cond [(= k 0) 1] [else 0])]
[(>= k n) 0]
[else
(hash-table-get ht (list n k) (lambda ()
(let ([answer (apply + (apply append (build-list n (lambda (n1) (build-list (cond [(= k 0) 1] [else k])
(lambda (k1) (help n1 k1)))))))])
(begin (hash-table-put! ht (list n k) answer)
answer))))])))
(cond
[(>= k n) 0]
[else (apply + (apply append (build-list (add1 n) (lambda (n1) (build-list (add1 k) (lambda (k1) (help n1 k1)))))))])))
|
|
CROSSREFS
|
Sequence in context: A005250 A162762 A156097 this_sequence A000937 A167229 A068902
Adjacent sequences: A039594 A039595 A039596 this_sequence A039598 A039599 A039600
|
|
KEYWORD
|
nonn,easy,tabl
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
EXTENSIONS
|
More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), Jun 22 2006
|
|
|
Search completed in 0.002 seconds
|
