A188122 Table read by downward antidiagonals: T(n,k) is the number of strictly increasing arrangements of n nonzero numbers in -(n+k-2)..(n+k-2) with sum zero.

0, 0, 1, 0, 2, 0, 0, 3, 2, 3, 0, 4, 4, 8, 4, 0, 5, 8, 16, 16, 16, 0, 6, 12, 31, 42, 52, 42, 0, 7, 18, 51, 90, 137, 152, 137, 0, 8, 24, 80, 172, 308, 426, 484, 426, 0, 9, 32, 118, 296, 624, 1032, 1398, 1536, 1398, 0, 10, 40, 167, 482, 1154, 2216, 3528, 4622, 5064, 4622, 0, 11, 50

Offset: 1

Author

R. H. Hardin, Mar 21 2011

Keywords

• nonn
• tabl

Comments

Table starts

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, ...

0, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, ...

3, 8, 16, 31, 51, 80, 118, 167, 227, 302, 390, ...

4, 16, 42, 90, 172, 296, 482, 740, 1092, 1554, 2154, ...

16, 52, 137, 308, 624, 1154, 1999, 3278, 5144, 7772, 11387, ...

42, 152, 426, 1032, 2216, 4376, 8044, 13994, 23210, 37030, 57086, ...

137, 484, 1398, 3528, 7970, 16547, 32035, 58595, 102113, 170844, 275878, ...

426, 1536, 4622, 12124, 28660, 62222, 126122, 241250, 439514, 767656, 1292864, ...

1398, 5064, 15594, 42262, 103599, 233880, 493267, 982016, 1861168, 3379972, 5913676, ...

Examples

			Some solutions for n=8, k=6:
  -11 -12 -11 -11 -12 -10 -11 -12 -12  -9 -10 -11 -11 -12 -12  -7
   -9  -9 -10  -8  -6  -8  -9 -11  -9  -5  -8 -10  -8 -10 -10  -6
   -5  -8  -4  -4  -4  -5  -8  -4  -8  -4  -5  -4  -7  -9  -5  -5
   -4  -3  -2  -2  -1  -3  -3  -2   1  -2  -3  -1   1   1  -2  -3
    2   5   2   1   2  -1   1  -1   4   1   4   3   2   2   3  -2
    6   8   4   6   4   8   7   7   5   2   5   4   6   8   5   5
    9   9  10   7   5   9  11  11   9   8   8   8   7   9   9   8
   12  10  11  11  12  10  12  12  10   9   9  11  10  11  12  10
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..550
• Louis Ng, Magic counting with inside-out polytopes, Master's Thesis, San Francisco State University, 2018.

Crossrefs

Row 3 is A007590.