A183917 - OEIS

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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

(list; table; graph; refs; listen; history; text; internal format)

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

PROG

(Python)

from sympy.utilities.iterables import partitions

def A183917_T(n, k): return sum(1 for p in partitions(k*n, m=n, k=k<<1)) # Chai Wah Wu, Aug 27 2024

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