A183917 T(n,k) = number of nondecreasing arrangements of n numbers in -k..k with sum zero.

1, 1, 2, 1, 3, 2, 1, 4, 5, 3, 1, 5, 8, 8, 3, 1, 6, 13, 18, 12, 4, 1, 7, 18, 33, 32, 18, 4, 1, 8, 25, 55, 73, 58, 24, 5, 1, 9, 32, 86, 141, 151, 94, 33, 5, 1, 10, 41, 126, 252, 338, 289, 151, 43, 6, 1, 11, 50, 177, 414, 676, 734, 526, 227, 55, 6, 1, 12, 61, 241, 649, 1242, 1656, 1514

Offset

1,3

Links

R. H. Hardin, Table of n, a(n) for n = 1..1350

David J. Hemmer and Karlee J. Westrem, Palindrome Partitions and the Calkin-Wilf Tree, arXiv:2402.02250 [math.CO], 2024. See Definition 5.1 p. 8.

Example

Table starts
 1  1   1    1    1     1     1      1      1      1       1       1       1
 2  3   4    5    6     7     8      9     10     11      12      13      14
 2  5   8   13   18    25    32     41     50     61      72      85      98
 3  8  18   33   55    86   126    177    241    318     410     519     645
 3 12  32   73  141   252   414    649    967   1394    1944    2649    3523
 4 18  58  151  338   676  1242   2137   3486   5444    8196   11963   17002
 4 24  94  289  734  1656  3370   6375  11322  19138   30982   48417   73316
 5 33 151  526 1514  3788  8512  17575  33885  61731  107233  178870  288100
 5 43 227  910 2934  8150 20094  45207  94257 184717  343363  610358 1043534
 6 55 338 1514 5448 16660 44916 109583 246448 517971 1028172 1943488 3521260
Some solutions for n=5:
  -2  -4  -4  -4  -4  -1  -4  -3  -4  -3  -1  -4  -3  -3  -2  -4
  -2   0   0  -1  -2   0  -2  -2  -1  -3  -1  -4   0  -2   0  -3
   0   0   0   0  -1   0   1  -1   1   0   0   1   0   1   0  -1
   0   1   2   2   3   0   2   3   2   3   0   3   0   1   1   4
   4   3   2   3   4   1   3   3   2   3   2   4   3   3   1   4

Crossrefs

Column 2 is A001973.

Column 3 is A001977.

Column 4 is A001981.

Diagonal is A109655.

Row 3 is A000982(n+1).

Sequence in context: A341315 A293600 A191395 * A181971 A104741 A167237

Adjacent sequences: A183914 A183915 A183916 * A183918 A183919 A183920

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 07 2011

Status

approved