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

1,5

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, ...

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.

Example

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

Crossrefs

Row 3 is A007590.

Sequence in context: A205341 A195664 A053202 * A341841 A050186 A334218

Adjacent sequences: A188119 A188120 A188121 * A188123 A188124 A188125

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 21 2011

Status

approved