A192710 -id:A192710 - cp's OEIS frontend

A192691 Number of 1X4 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 <= 2n^2 (number of collections of 1 zero-sum 4-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

2, 6, 15, 26, 45, 72, 105, 150, 206, 273, 353, 446, 560, 687, 834, 998, 1182, 1388, 1618, 1875, 2156, 2463, 2797, 3151, 3551, 3978, 4434, 4923, 5448, 6009, 6604, 7243, 7925, 8639, 9404, 10198, 11051, 11943, 12887, 13873, 14909, 16001, 17135, 18332, 19584

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (1,4,n) of A192710

			Some solutions for 1X4 <= 2*4^2
.-1..0..0..1...-2..0..0..2...-1.-1.-1..3...-2..0..1..1...-3.-1..0..4

R. H. Hardin, Table of n, a(n) for n = 1..200

A192692 Number of 1X5 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 <= 2n^2 (number of collections of 1 zero-sum 5-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 8, 21, 48, 93, 170, 285, 452, 674, 985, 1379, 1894, 2524, 3307, 4272, 5414, 6790, 8406, 10290, 12475, 14998, 17857, 21159, 24847, 29047, 33708, 38944, 44737, 51180, 58301, 66094, 74687, 84097, 94333, 105510, 117600, 130807, 144983, 160325, 176837

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (1,5,n) of A192710

			Some solutions for 1X5 <= 2*4^2
.-2.-1..1..1..1...-2.-1..0..1..2...-1.-1..0..1..1...-2..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..200

A192693 Number of 1X6 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 <= 2n^2 (number of collections of 1 zero-sum 6-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 9, 28, 78, 171, 350, 650, 1142, 1868, 2949, 4454, 6554, 9361, 13071, 17829, 23929, 31576, 41080, 52705, 66899, 83871, 104326, 128432, 156793, 190022, 228672, 273250, 324752, 383434, 450569, 526647, 612832, 709667, 818736, 940570, 1076447, 1227802

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (1,6,n) of A192710

			Some solutions for 1X6 <= 2*4^2
.-3.-2..0..0..2..3...-3.-1..0..0..2..2...-3.-1.-1.-1..3..3...-3.-2.-1..1..2..3

R. H. Hardin, Table of n, a(n) for n = 1..200

A192694 Number of 1X7 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 <= 2n^2 (number of collections of 1 zero-sum 7-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 9, 36, 110, 277, 634, 1304, 2492, 4430, 7559, 12260, 19272, 29251, 43339, 62515, 88501, 122666, 167322, 224735, 297919, 389439, 504010, 644682, 817003, 1025762, 1278054, 1578938, 1938210, 2360862, 2859571, 3441853, 4122058, 4907573, 5817118

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (1,7,n) of A192710

			Some solutions for 1X7 <= 2*4^2
.-2.-2.-2..0..1..1..4...-2.-2.-1..0..1..2..2...-2.-2..0..1..1..1..1

R. H. Hardin, Table of n, a(n) for n = 1..141

A192695 Number of 1X8 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 <= 2n^2 (number of collections of 1 zero-sum 8-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 10, 42, 147, 415, 1040, 2336, 4841, 9324, 17035, 29556, 49428, 79553, 124531, 189360, 281680, 409383, 584737, 819889, 1133021, 1541844, 2072913, 2751299, 3615478, 4697427, 6051068, 7720384, 9776322, 12276825, 15316939, 18967552

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (1,8,n) of A192710

			Some solutions for 1X8 <= 2*4^2
.-4.-1..0..0..1..1..1..2...-3.-1.-1.-1..0..0..3..3...-3.-3.-1..0..1..2..2..2

R. H. Hardin, Table of n, a(n) for n = 1..90

A192696 Number of 1X9 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 <= 2n^2 (number of collections of 1 zero-sum 9-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 10, 48, 185, 577, 1570, 3840, 8577, 17690, 34551, 63830, 112942, 192361, 317003, 506670, 789958, 1201985, 1791493, 2619745, 3765999, 5326330, 7428899, 10220081, 13894828, 18669185, 24830564, 32689442, 42659878, 55175883, 70815315, 90176720

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (1,9,n) of A192710

			Some solutions for 1X9 <= 2*4^2
.-3.-2..0..0..1..1..1..1..1...-2.-2.-1.-1.-1..0..1..3..3

R. H. Hardin, Table of n, a(n) for n = 1..68

A192697 Number of 1X10 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 <= 2n^2 (number of collections of 1 zero-sum 10-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 10, 54, 223, 758, 2239, 5888, 14055, 30973, 64220, 125681, 234793, 421151, 728848, 1221122, 1990599, 3162071, 4910443, 7471318, 11154759, 16368766, 23649285, 33671936, 47306193, 65642371, 90041983, 122175046, 164141152, 218451247

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (1,10,n) of A192710

			Some solutions for 1X10 <= 2*4^2
.-3.-2.-1.-1.-1..1..1..2..2..2...-3.-2.-2..0..0..1..1..1..1..3

R. H. Hardin, Table of n, a(n) for n = 1..53

A192698 Number of 2X3 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 <= 2n^2 (number of collections of 2 zero-sum 3-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 8, 20, 54, 104, 190, 323, 529, 795, 1181, 1653, 2297, 3088, 4119, 5307, 6804, 8518, 10618, 13029, 15955, 19160, 22996, 27203, 32102, 37584, 43811, 50621, 58445, 66858, 76327, 86710, 98294, 110610, 124474, 139222, 155502, 173011, 192273, 212726

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (2,3,n) of A192710

			Some solutions for 2X3 <= 2*4^2
.-3..0..3...-1..0..1...-2.-1..3...-2.-1..3...-2.-2..4...-1.-1..2...-1.-1..2
.-3..1..2....0..0..0...-2..1..1...-2.-1..3...-1.-1..2....0..0..0...-1.-1..2

R. H. Hardin, Table of n, a(n) for n = 1..200

A192699 Number of 2X4 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 <= 2n^2 (number of collections of 2 zero-sum 4-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 11, 48, 166, 459, 1125, 2426, 4871, 9028, 15919, 26530, 42795, 66234, 100066, 146708, 211012, 295903, 409009, 555042, 743702, 980297, 1279677, 1648401, 2106146, 2660304, 3336122, 4142715, 5114735, 6259510, 7619959, 9210010

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (2,4,n) of A192710

			Some solutions for 2X4 <= 2*4^2
.-3.-1..1..3...-3.-1..2..2...-1.-1..0..2...-2.-1..0..3...-2.-2..1..3
.-3..1..1..1...-2.-1..0..3....0..0..0..0...-2..0..0..2...-2..0..0..2

R. H. Hardin, Table of n, a(n) for n = 1..120

A192700 Number of 2X5 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 <= 2n^2 (number of collections of 2 zero-sum 5-vectors with total modulus squared not more than 2n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 13, 75, 361, 1355, 4257, 11487, 28113, 62690, 130088, 253378, 470284, 832594, 1423302, 2347627, 3764623, 5870541, 8958955, 13369172, 19590712, 28190894, 39941879, 55749068, 76863446, 104549377, 140705757, 187241581, 246861965

Offset: 1

R. H. Hardin Jul 07 2011

nonn

Column (2,5,n) of A192710

			Some solutions for 2X5 <= 2*4^2
.-3.-1..0..1..3...-2.-2..1..1..2...-2.-1.-1..2..2...-2.-1..1..1..1
.-2.-1..0..1..2...-2..0..0..0..2...-1.-1..0..1..1...-2..0..0..1..1

R. H. Hardin, Table of n, a(n) for n = 1..56

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