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.

Showing 1-6 of 6 results.

A223772 Number of n X 3 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

7, 28, 78, 180, 371, 707, 1269, 2170, 3563, 5650, 8692, 13020, 19047, 27281, 38339, 52962, 72031, 96584, 127834, 167188, 216267, 276927, 351281, 441722, 550947, 681982, 838208, 1023388, 1241695, 1497741, 1796607, 2143874, 2545655, 3008628
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Comments

Column 3 of A223777.

Examples

			Some solutions for n=3:
..0..1..1....1..0..0....1..1..1....1..0..0....1..0..0....0..0..0....0..1..0
..1..1..0....1..0..0....1..1..1....1..0..0....1..0..0....0..1..0....1..1..0
..1..0..0....0..0..0....1..1..1....1..1..0....1..1..1....1..1..1....1..0..0

Links

Crossrefs

Cf. A223777.

Formula

Empirical: a(n) = (1/720)*n^6 + (1/80)*n^5 + (29/144)*n^4 + (25/48)*n^3 + (1727/360)*n^2 - (8/15)*n + 2.
Conjectures from Colin Barker, Aug 23 2018: (Start)
G.f.: x*(7 - 21*x + 29*x^2 - 23*x^3 + 14*x^4 - 7*x^5 + 2*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A223773 Number of n X 4 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

11, 56, 180, 461, 1040, 2164, 4246, 7950, 14308, 24877, 41945, 68796, 110045, 172055, 263449, 395731, 584031, 847990, 1212802, 1710431, 2381022, 3274526, 4452560, 5990524, 7979998, 10531443, 13777231, 17875030, 23011571, 29406825, 37318619
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Comments

Column 4 of A223777.

Examples

			Some solutions for n=3:
..1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..1..0..0
..0..0..1..0....0..0..1..1....1..1..0..0....0..1..0..0....1..1..0..0
..0..1..1..1....0..1..1..0....1..1..0..0....1..1..0..0....1..0..0..0

Links

Crossrefs

Cf. A223777.

Formula

Empirical: a(n) = (1/40320)*n^8 + (1/3360)*n^7 + (19/2880)*n^6 + (7/120)*n^5 + (2447/5760)*n^4 + (259/160)*n^3 + (126691/10080)*n^2 - (12329/840)*n + 13 for n>1.
Conjectures from Colin Barker, Aug 23 2018: (Start)
G.f.: x*(11 - 43*x + 72*x^2 - 67*x^3 + 53*x^4 - 50*x^5 + 34*x^6 - 6*x^7 - 5*x^8 + 2*x^9) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>10.
(End)

A223774 Number of n X 5 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

16, 101, 371, 1040, 2516, 5573, 11635, 23230, 44703, 83305, 150815, 265901, 457485, 769447, 1267085, 2045843, 3242928, 5052561, 7745747, 11695606, 17409482, 25569241, 37081383, 53138828, 75296493, 105563057, 146511615, 201412251
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Comments

Column 5 of A223777.

Examples

			Some solutions for n=3:
..0..0..0..0..0....1..0..0..0..0....1..0..0..0..0....0..0..0..0..0
..1..0..0..0..0....1..0..0..0..0....0..0..0..0..1....0..0..0..0..0
..0..0..0..0..1....0..0..1..1..1....0..0..0..1..0....0..0..1..1..0

Links

Crossrefs

Cf. A223777.

Formula

Empirical: a(n) = (1/3628800)*n^10 + (1/241920)*n^9 + (1/8640)*n^8 + (11/8064)*n^7 + (4273/172800)*n^6 + (589/11520)*n^5 + (649763/362880)*n^4 + (589/12096)*n^3 + (102443/2400)*n^2 - (16061/168)*n + 93 for n>2.
Conjectures from Colin Barker, Aug 23 2018: (Start)
G.f.: x*(16 - 75*x + 140*x^2 - 126*x^3 + 96*x^4 - 180*x^5 + 272*x^6 - 200*x^7 + 65*x^8 - 20*x^9 + 27*x^10 - 18*x^11 + 4*x^12) / (1 - x)^11.
a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>13.
(End)

A223775 Number of n X 6 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

22, 169, 707, 2164, 5573, 12975, 28346, 59231, 119555, 234348, 447489, 834107, 1520016, 2711565, 4740623, 8131175, 13696273, 22676975, 36938539, 59243658, 93628083, 145910759, 224378788, 340697347, 511106363, 757979538, 1111837505
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Column 6 of A223777.

Examples

			Some solutions for n=3
..0..0..0..0..0..1....0..0..0..0..0..1....0..0..0..0..0..0....0..0..0..0..0..0
..0..0..1..1..1..1....0..0..0..1..1..0....0..0..0..0..1..0....0..0..0..0..0..0
..0..1..1..1..1..0....1..1..1..1..1..0....1..1..1..1..1..1....0..1..1..1..1..0

Links

Crossrefs

Cf. A223777.

Formula

Empirical: a(n) = (1/479001600)*n^12 + (1/26611200)*n^11 + (11/8709120)*n^10 + (1/53760)*n^9 + (6271/14515200)*n^8 + (493/115200)*n^7 + (320657/8709120)*n^6 + (157151/483840)*n^5 + (41441549/10886400)*n^4 - (451279/67200)*n^3 + (49282619/332640)*n^2 - (20927/44)*n + 563 for n>3.

A223776 Number of nX7 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

29, 267, 1269, 4246, 11635, 28346, 64256, 138913, 290180, 589799, 1170809, 2274787, 4331570, 8091182, 14838137, 26733456, 47351379, 82508140, 141522193, 239102564, 398139077, 653770622, 1059242178, 1694236163, 2676588670, 4178587937
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Column 7 of A223777

Examples

			Some solutions for n=3
..0..1..0..0..0..0..0....0..0..0..0..1..1..0....0..0..0..0..0..0..0
..1..1..1..1..1..1..0....0..0..0..1..1..1..0....0..0..0..0..1..1..1
..1..1..1..1..1..1..0....0..0..1..1..1..1..1....1..1..1..1..1..1..1

Links

Formula

Empirical: a(n) = (1/87178291200)*n^14 + (1/4151347200)*n^13 + (1/106444800)*n^12 + (53/319334400)*n^11 + (409/87091200)*n^10 + (1681/29030400)*n^9 + (862999/609638400)*n^8 - (56411/29030400)*n^7 + (3673639/14515200)*n^6 - (4250857/7257600)*n^5 + (1960444733/119750400)*n^4 - (326164913/4989600)*n^3 + (89807927381/151351200)*n^2 - (113103797/51480)*n + 3030 for n>4

A223771 Number of n X n 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.

Original entry on oeis.org

2, 12, 78, 461, 2516, 12975, 64256, 308895, 1451996, 6707709, 30563338, 137715999, 614855772, 2724027619
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Diagonal of A223777

Examples

			Some solutions for n=3
..0..1..0....0..0..0....1..0..0....0..0..1....0..0..0....0..0..0....0..0..0
..1..0..0....0..0..0....1..1..0....1..1..1....1..1..0....1..0..0....0..0..0
..1..0..0....1..0..0....1..1..1....1..1..1....1..1..0....0..0..1....0..1..1
Showing 1-6 of 6 results.

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