cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A192701 Number of 3X2 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 3 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, 5, 10, 16, 27, 42, 58, 80, 110, 143, 182, 226, 281, 343, 413, 489, 576, 676, 783, 901, 1035, 1172, 1328, 1493, 1674, 1872, 2086, 2308, 2544, 2805, 3069, 3364, 3679, 4000, 4348, 4709, 5096, 5493, 5926, 6366, 6832, 7330, 7841, 8380, 8950, 9528, 10134, 10766
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (3,2,n) of A192710

Examples

			Some solutions for 3X2 <= 2*4^2
.-3..3...-1..1...-1..1...-4..4...-2..2...-2..2...-3..3...-2..2...-3..3....0..0
.-1..1....0..0...-1..1....0..0...-1..1...-2..2...-2..2...-1..1...-1..1....0..0
..0..0....0..0...-1..1....0..0...-1..1....0..0....0..0....0..0...-1..1....0..0

Links

A192702 Number of 3X3 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 3 zero-sum 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 9, 36, 114, 308, 745, 1597, 3194, 5944, 10408, 17408, 28207, 43739, 66091, 97417, 139756, 197048, 273225, 370834, 497159, 658332, 859295, 1109567, 1420234, 1795384, 2253449, 2806737, 3464221, 4246712, 5179322, 6262896, 7537671, 9025226
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (3,3,n) of A192710

Examples

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

Links

A192703 Number of 4X2 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 4 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, 12, 23, 41, 70, 106, 159, 230, 323, 436, 578, 757, 975, 1232, 1536, 1889, 2317, 2797, 3355, 3994, 4711, 5523, 6438, 7465, 8618, 9888, 11296, 12839, 14557, 16398, 18449, 20689, 23115, 25758, 28591, 31673, 34995, 38586, 42415, 46528, 50984, 55687
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (4,2,n) of A192710

Examples

			Some solutions for 4X2 <= 2*4^2
.-3..3...-3..3...-1..1...-2..2...-3..3...-2..2...-2..2...-1..1...-1..1...-2..2
..0..0...-1..1...-1..1...-2..2...-2..2...-2..2....0..0...-1..1...-1..1...-2..2
..0..0...-1..1....0..0....0..0...-1..1...-2..2....0..0...-1..1...-1..1...-2..2
..0..0....0..0....0..0....0..0....0..0...-1..1....0..0...-1..1....0..0...-2..2

Links

A192704 Number of 4X3 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 4 zero-sum 3-vectors with total modulus squared not more than 2*n^2, ignoring vector and component permutations).

Original entry on oeis.org

2, 10, 45, 191, 639, 1925, 5059, 12197, 27061, 55957, 109220, 204227, 361922, 621790, 1032797, 1662821, 2607574, 4007507, 5999290, 8835971, 12784870, 18186200, 25491781, 35326689, 48192368, 65114102, 87009836, 115061673, 150717188
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (4,3,n) of A192710

Examples

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

Links

A192705 Number of 5X2 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 5 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, 14, 29, 56, 101, 166, 267, 407, 604, 865, 1211, 1659, 2236, 2956, 3861, 4949, 6299, 7906, 9849, 12120, 14817, 17958, 21641, 25859, 30753, 36318, 42732, 49917, 58116, 67296, 77693, 89219, 102175, 116527, 132515, 150117, 169602, 191013, 214662
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (5,2,n) of A192710

Examples

			Some solutions for 5X2 <= 2*4^2
.-3..3...-2..2...-2..2...-1..1...-1..1...-2..2...-3..3...-3..3...-3..3...-2..2
.-1..1...-1..1...-2..2...-1..1...-1..1...-2..2...-1..1....0..0...-1..1...-2..2
.-1..1...-1..1...-1..1....0..0...-1..1...-2..2...-1..1....0..0....0..0...-2..2
.-1..1....0..0...-1..1....0..0....0..0...-2..2...-1..1....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

Links

A192706 Number of 6X2 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 6 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, 16, 34, 71, 135, 235, 396, 641, 993, 1496, 2193, 3136, 4398, 6065, 8214, 10949, 14438, 18760, 24151, 30736, 38755, 48448, 60129, 73970, 90426, 109793, 132568, 158991, 189853, 225331, 266394, 313294, 367015, 428094, 497667, 575969, 664608
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (6,2,n) of A192710

Examples

			Some solutions for 6X2 <= 2*4^2
.-2..2...-3..3...-1..1...-1..1...-2..2...-2..2...-3..3...-3..3...-1..1...-1..1
.-2..2...-2..2...-1..1...-1..1...-1..1...-2..2....0..0...-1..1...-1..1....0..0
.-1..1...-1..1....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1....0..0
..0..0....0..0....0..0....0..0...-1..1...-1..1....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....0..0....0..0

Links

A192707 Number of 7X2 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 7 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, 17, 39, 85, 167, 309, 546, 919, 1486, 2338, 3564, 5300, 7703, 11016, 15451, 21303, 28978, 38908, 51626, 67686, 87827, 112967, 144076, 182028, 228322, 284414, 351962, 432504, 528554, 642212, 776430, 933563, 1117263, 1331217, 1579771, 1865945
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (7,2,n) of A192710

Examples

			Some solutions for 7X2 <= 2*4^2
.-1..1...-3..3...-2..2...-3..3...-3..3...-2..2...-2..2...-2..2...-2..2...-2..2
.-1..1....0..0...-1..1...-1..1...-1..1...-1..1...-1..1....0..0...-2..2...-2..2
.-1..1....0..0...-1..1....0..0...-1..1...-1..1....0..0....0..0...-2..2....0..0
.-1..1....0..0...-1..1....0..0...-1..1...-1..1....0..0....0..0...-1..1....0..0
.-1..1....0..0....0..0....0..0...-1..1...-1..1....0..0....0..0...-1..1....0..0
.-1..1....0..0....0..0....0..0...-1..1...-1..1....0..0....0..0...-1..1....0..0
..0..0....0..0....0..0....0..0....0..0...-1..1....0..0....0..0....0..0....0..0

Links

A192708 Number of 8X2 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 8 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, 18, 43, 97, 199, 385, 707, 1235, 2072, 3383, 5336, 8218, 12341, 18215, 26362, 37488, 52464, 72546, 98944, 133305, 177633, 234514, 306557, 397175, 510188, 650637, 823774, 1035586, 1293255, 1606070, 1982596, 2433768, 2972209, 3612860
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (8,2,n) of A192710

Examples

			Some solutions for 8X2 <= 2*4^2
.-1..1...-2..2...-1..1...-1..1...-1..1...-1..1...-3..3...-3..3...-2..2...-1..1
.-1..1...-1..1...-1..1....0..0...-1..1...-1..1...-1..1...-2..2...-2..2...-1..1
.-1..1...-1..1....0..0....0..0...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1
..0..0...-1..1....0..0....0..0...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1
..0..0...-1..1....0..0....0..0...-1..1...-1..1...-1..1...-1..1...-1..1...-1..1
..0..0....0..0....0..0....0..0...-1..1...-1..1...-1..1....0..0...-1..1...-1..1
..0..0....0..0....0..0....0..0....0..0...-1..1....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...-1..1

Links

A192709 Number of 9X2 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 9 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, 46, 108, 231, 460, 872, 1581, 2737, 4607, 7508, 11904, 18426, 27989, 41631, 60856, 87536, 124153, 173696, 239976, 327657, 442880, 592595, 785351, 1031659, 1344609, 1738831, 2232241, 2845802, 3605355, 4538949, 5681318, 7071215, 8756412
Offset: 1

Views

Author

R. H. Hardin Jul 07 2011

Keywords

Comments

Column (9,2,n) of A192710

Examples

			Some solutions for 9X2 <= 2*4^2
.-2..2...-3..3...-2..2...-2..2...-1..1...-2..2...-2..2....0..0...-3..3...-1..1
.-1..1...-2..2...-2..2...-2..2...-1..1...-1..1...-1..1....0..0...-2..2...-1..1
.-1..1...-1..1...-2..2...-2..2...-1..1...-1..1...-1..1....0..0...-1..1...-1..1
.-1..1...-1..1...-1..1...-1..1....0..0...-1..1...-1..1....0..0...-1..1...-1..1
.-1..1...-1..1....0..0...-1..1....0..0...-1..1...-1..1....0..0....0..0...-1..1
.-1..1....0..0....0..0...-1..1....0..0....0..0...-1..1....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
..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...-1..1

Links

A192711 Number of 10 X 2 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 10 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, 49, 118, 259, 534, 1042, 1941, 3465, 5996, 10040, 16364, 26012, 40522, 61835, 92657, 136556, 198316, 283977, 401349, 560438, 774140, 1058263, 1432174, 1920672, 2554179, 3369134, 4409927, 5730887, 7397192, 9486111, 12090252, 15318436
Offset: 1

Views

Author

R. H. Hardin, Jul 07 2011

Keywords

Comments

Column (10,2,n) of A192710.

Examples

			Some solutions for 10 X 2 <= 2*4^2
.-2..2...-3..3...-2..2...-1..1....0..0...-2..2...-3..3...-1..1...-3..3...-2..2
.-1..1...-2..2...-2..2...-1..1....0..0...-2..2...-2..2....0..0...-1..1...-1..1
.-1..1...-1..1...-2..2...-1..1....0..0...-2..2...-1..1....0..0....0..0...-1..1
.-1..1...-1..1...-1..1....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....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
..0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0....0..0

Links

Crossrefs

Cf. A192710.
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