A188122 - OEIS

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.

%I #15 Dec 14 2019 21:28:33

%S 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,

%T 18,51,90,137,152,137,0,8,24,80,172,308,426,484,426,0,9,32,118,296,

%U 624,1032,1398,1536,1398,0,10,40,167,482,1154,2216,3528,4622,5064,4622,0,11,50

%N 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.

%C Table starts

%C 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...

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

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

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

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

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

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

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

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

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

%H R. H. Hardin, <a href="/A188122/b188122.txt">Table of n, a(n) for n = 1..550</a>

%H Louis Ng, <a href="http://math.sfsu.edu/beck/teach/masters/louis.pdf">Magic counting with inside-out polytopes</a>, Master's Thesis, San Francisco State University, 2018.

%e Some solutions for n=8, k=6:

%e -11 -12 -11 -11 -12 -10 -11 -12 -12 -9 -10 -11 -11 -12 -12 -7

%e -9 -9 -10 -8 -6 -8 -9 -11 -9 -5 -8 -10 -8 -10 -10 -6

%e -5 -8 -4 -4 -4 -5 -8 -4 -8 -4 -5 -4 -7 -9 -5 -5

%e -4 -3 -2 -2 -1 -3 -3 -2 1 -2 -3 -1 1 1 -2 -3

%e 2 5 2 1 2 -1 1 -1 4 1 4 3 2 2 3 -2

%e 6 8 4 6 4 8 7 7 5 2 5 4 6 8 5 5

%e 9 9 10 7 5 9 11 11 9 8 8 8 7 9 9 8

%e 12 10 11 11 12 10 12 12 10 9 9 11 10 11 12 10

%Y Row 3 is A007590.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Mar 21 2011