A192712
Number of 11X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 11 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
Original entry on oeis.org
2, 6, 19, 51, 126, 285, 604, 1208, 2310, 4237, 7513, 12885, 21536, 35072, 55893, 87271, 133793, 201572, 299171, 437546, 631447, 900231, 1268643, 1768448, 2440754, 3336495, 4520239, 6073339, 8095214, 10708816, 14066591, 18351402, 23788458
Offset: 1
Some solutions for 11X2 <= 2*4^2
.-1..1...-3..3...-3..3...-3..3...-2..2...-1..1...-2..2...-3..3...-2..2...-3..3
..0..0...-2..2...-1..1...-2..2...-2..2...-1..1...-1..1...-1..1...-2..2...-1..1
..0..0...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1...-2..2...-1..1
..0..0...-1..1...-1..1...-1..1...-1..1....0..0...-1..1...-1..1...-1..1....0..0
..0..0....0..0...-1..1...-1..1...-1..1....0..0...-1..1....0..0....0..0....0..0
..0..0....0..0....0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0
..0..0....0..0....0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0...-1..1....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
A192713
Number of 12X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 12 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
Original entry on oeis.org
2, 6, 19, 53, 133, 310, 669, 1371, 2684, 5037, 9125, 16021, 27343, 45523, 74103, 118121, 184828, 284258, 430192, 641623, 944008, 1371445, 1968786, 2795325, 3927604, 5465114, 7534219, 10297413, 13958709, 18775675, 25067921, 33235421
Offset: 1
Some solutions for 12X2 <= 2*4^2
.-2..2...-2..2...-2..2...-1..1...-2..2...-2..2...-1..1....0..0...-2..2...-1..1
.-1..1...-1..1...-1..1...-1..1...-1..1...-2..2...-1..1....0..0...-1..1...-1..1
.-1..1...-1..1...-1..1...-1..1...-1..1...-2..2...-1..1....0..0...-1..1....0..0
.-1..1...-1..1...-1..1...-1..1...-1..1....0..0...-1..1....0..0...-1..1....0..0
..0..0...-1..1...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
..0..0....0..0...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
..0..0....0..0...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
..0..0....0..0...-1..1...-1..1...-1..1....0..0....0..0....0..0...-1..1....0..0
..0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0
..0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0
..0..0....0..0....0..0....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1....0..0
A192714
Number of 13X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 13 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
Original entry on oeis.org
2, 6, 19, 55, 140, 331, 732, 1533, 3055, 5857, 10824, 19386, 33743, 57293, 95044, 154445, 246197, 385697, 594416, 902641, 1351643, 1998191, 2918046, 4213843, 6019994, 8515367, 11930845, 16568416, 22815114, 31168260, 42253487, 56871045
Offset: 1
Some solutions for 13X2 <= 2*4^2
.-3..3...-2..2...-2..2...-2..2...-2..2...-2..2...-3..3...-2..2...-2..2...-3..3
.-1..1....0..0...-2..2...-2..2...-2..2...-2..2...-1..1...-1..1...-1..1...-2..2
.-1..1....0..0...-1..1...-2..2...-2..2....0..0...-1..1...-1..1...-1..1...-1..1
.-1..1....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1...-1..1...-1..1
.-1..1....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1...-1..1....0..0
.-1..1....0..0...-1..1...-1..1....0..0....0..0...-1..1...-1..1...-1..1....0..0
.-1..1....0..0...-1..1...-1..1....0..0....0..0....0..0...-1..1...-1..1....0..0
..0..0....0..0...-1..1....0..0....0..0....0..0....0..0...-1..1...-1..1....0..0
..0..0....0..0...-1..1....0..0....0..0....0..0....0..0...-1..1....0..0....0..0
..0..0....0..0...-1..1....0..0....0..0....0..0....0..0...-1..1....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
A192715
Number of 14X2 integer matrices with each row summing to zero, row elements in nondecreasing order, rows in lexicographically nondecreasing order, and the sum of squares of the elements <= 2*n^2 (number of collections of 14 zero-sum 2-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).
Original entry on oeis.org
2, 6, 19, 56, 146, 350, 790, 1685, 3421, 6680, 12575, 22923, 40636, 70228, 118550, 196038, 317911, 506487, 793842, 1225546, 1865180, 2802329, 4157823, 6098617, 8848923, 12709523, 18076665, 25480353, 35605456, 49349547, 67866426, 92643950
Offset: 1
Some solutions for 14X2 <= 2*4^2
.-2..2...-3..3...-3..3...-2..2...-2..2...-2..2...-3..3...-3..3...-1..1...-1..1
.-1..1...-1..1...-1..1...-2..2...-2..2...-1..1...-2..2...-1..1...-1..1...-1..1
.-1..1...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1....0..0...-1..1...-1..1
.-1..1....0..0...-1..1...-1..1...-1..1...-1..1....0..0....0..0...-1..1...-1..1
.-1..1....0..0...-1..1...-1..1....0..0...-1..1....0..0....0..0...-1..1...-1..1
.-1..1....0..0...-1..1....0..0....0..0...-1..1....0..0....0..0...-1..1...-1..1
.-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1...-1..1
.-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1...-1..1
.-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1
.-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0...-1..1
.-1..1....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0
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