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A183917 T(n,k) = number of nondecreasing arrangements of n numbers in -k..k with sum zero. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 07 2011
STATUS
approved

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Last modified May 19 10:22 EDT 2024. Contains 372683 sequences. (Running on oeis4.)