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 1-10 of 11 results. Next

A224033 Number of n X 3 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

4, 13, 37, 105, 298, 848, 2419, 6908, 19737, 56401, 161181, 460622, 1316360, 3761867, 10750568, 30722673, 87798365, 250907593, 717036338, 2049125344, 5855930115, 16734904820, 47824518777, 136671503209, 390575802373, 1116176041318
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Column 3 of A224038.

Examples

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

Links

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) - a(n-3) + 2*a(n-5).
Empirical g.f.: x*(1 - x)*(4 + x - 2*x^2 - 2*x^3) / (1 - 4*x + 3*x^2 + x^3 - 2*x^5). - Colin Barker, Aug 26 2018

A224034 Number of nX4 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

5, 19, 58, 168, 488, 1422, 4160, 12214, 35960, 106072, 313246, 925694, 2736638, 8092056, 23930330, 70772252, 209309684, 619043562, 1830861726, 5414905178, 16014983408, 47365507554, 140087012360, 414317718488, 1225375238694
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Column 4 of A224038

Examples

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

Links

Formula

Empirical: a(n) = 5*a(n-1) -6*a(n-2) -a(n-3) +2*a(n-4) +2*a(n-5) -2*a(n-6) +4*a(n-7)

A224035 Number of n X 5 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

6, 26, 85, 252, 734, 2149, 6321, 18673, 55373, 164729, 491332, 1468446, 4395388, 13170815, 39497285, 118511408, 355728667, 1068051097, 3207330581, 9632722080, 28932821313, 86907496260, 261060029437, 784214341324, 2355790958452
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Column 5 of A224038.

Examples

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

Links

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = 6*a(n-1) - 10*a(n-2) + a(n-3) + 6*a(n-4) + a(n-5) - 4*a(n-6) + 4*a(n-7) - 4*a(n-8) + 8*a(n-9) for n>10.
Empirical g.f.: x*(6 - 10*x - 11*x^2 - 4*x^3 + 10*x^4 + 18*x^5 + 3*x^6 - 14*x^7 - 4*x^9) / ((1 - 2*x)*(1 - 4*x + 2*x^2 + 3*x^3 - x^5 + 2*x^6 + 4*x^8)). - Colin Barker, Aug 26 2018

A224036 Number of nX6 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

7, 34, 119, 363, 1064, 3107, 9125, 26928, 79800, 237348, 708163, 2118654, 6353180, 19088180, 57442255, 173085671, 522085599, 1576088206, 4761041486, 14389487483, 43507313943, 131587493711, 398081815019, 1204514245101, 3645147239577
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Column 6 of A224038

Examples

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

Links

Formula

Empirical: a(n) = 7*a(n-1) -15*a(n-2) +6*a(n-3) +11*a(n-4) -4*a(n-5) -7*a(n-6) +6*a(n-7) -6*a(n-8) +8*a(n-9) -8*a(n-10) +16*a(n-11) for n>13

A224037 Number of nX7 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

8, 43, 161, 508, 1505, 4395, 12856, 37808, 111683, 331170, 985275, 2939862, 8794582, 26369119, 79223520, 238443031, 718767456, 2169574122, 6556325043, 19832290886, 60040894419, 181897703946, 551397549898, 1672317703423, 5074042241500
Offset: 1

Views

Author

R. H. Hardin Mar 30 2013

Keywords

Comments

Column 7 of A224038

Examples

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

Links

Formula

Empirical: a(n) = 8*a(n-1) -21*a(n-2) +15*a(n-3) +15*a(n-4) -16*a(n-5) -9*a(n-6) +12*a(n-7) -8*a(n-8) +10*a(n-9) -12*a(n-10) +16*a(n-11) -16*a(n-12) +32*a(n-13) for n>16

A224039 Number of 3 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

8, 21, 37, 58, 85, 119, 161, 212, 273, 345, 429, 526, 637, 763, 905, 1064, 1241, 1437, 1653, 1890, 2149, 2431, 2737, 3068, 3425, 3809, 4221, 4662, 5133, 5635, 6169, 6736, 7337, 7973, 8645, 9354, 10101, 10887, 11713, 12580, 13489, 14441, 15437, 16478
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Row 3 of A224038.

Examples

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

Links

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = (1/6)*n^3 + 1*n^2 + (47/6)*n for n>1.
Conjectures from Colin Barker, Aug 26 2018: (Start)
G.f.: x*(8 - 11*x + x^2 + 4*x^3 - x^4) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>5.
(End)

A224040 Number of 4 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

16, 55, 105, 168, 252, 363, 508, 695, 933, 1232, 1603, 2058, 2610, 3273, 4062, 4993, 6083, 7350, 8813, 10492, 12408, 14583, 17040, 19803, 22897, 26348, 30183, 34430, 39118, 44277, 49938, 56133, 62895, 70258, 78257, 86928, 96308, 106435, 117348
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Row 4 of A224038.

Examples

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

Links

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (83/24)*n^2 + (89/4)*n - 3 for n>2.
Conjectures from Colin Barker, Aug 26 2018: (Start)
G.f.: x*(16 - 25*x - 10*x^2 + 33*x^3 - 8*x^4 - 8*x^5 + 3*x^6) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>7.
(End)

A224041 Number of 5 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

32, 144, 298, 488, 734, 1064, 1505, 2091, 2864, 3875, 5185, 6866, 9002, 11690, 15041, 19181, 24252, 30413, 37841, 46732, 57302, 69788, 84449, 101567, 121448, 144423, 170849, 201110, 235618, 274814, 319169, 369185, 425396, 488369, 558705, 637040
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Row 5 of A224038.

Examples

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

Links

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (25/24)*n^3 + (227/24)*n^2 + (1289/20)*n - 7 for n>3.
Conjectures from Colin Barker, Aug 26 2018: (Start)
G.f.: x*(32 - 48*x - 86*x^2 + 220*x^3 - 124*x^4 - 12*x^5 + 9*x^6 + 17*x^7 - 7*x^8) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>9.
(End)

A224042 Number of 6 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

64, 377, 848, 1422, 2149, 3107, 4395, 6124, 8439, 11527, 15626, 21035, 28125, 37351, 49265, 64530, 83935, 108411, 139048, 177113, 224069, 281595, 351607, 436280, 538071, 659743, 804390, 975463, 1176797, 1412639, 1687677, 2007070, 2376479
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Row 6 of A224038.

Examples

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

Links

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (35/144)*n^4 + (127/48)*n^3 + (1249/45)*n^2 + (3727/20)*n + 6 for n>4.
Conjectures from Colin Barker, Aug 26 2018: (Start)
G.f.: x*(64 - 71*x - 447*x^2 + 1163*x^3 - 952*x^4 + 97*x^5 + 216*x^6 - 72*x^7 + 33*x^8 - 45*x^9 + 15*x^10) / (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>11.
(End)

A224043 Number of 7 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.

Original entry on oeis.org

128, 987, 2419, 4160, 6321, 9125, 12856, 17875, 24623, 33686, 45837, 62087, 83746, 112495, 150470, 200359, 265513, 350072, 459107, 598779, 776516, 1001209, 1283428, 1635659, 2072563, 2611258, 3271625, 4076639, 5052726, 6230147, 7643410, 9331711
Offset: 1

Views

Author

R. H. Hardin, Mar 30 2013

Keywords

Comments

Row 7 of A224038.

Examples

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

Links

Crossrefs

Cf. A224038.

Formula

Empirical: a(n) = (1/5040)*n^7 + (17/360)*n^5 + (13/24)*n^4 + (5767/720)*n^3 + (1919/24)*n^2 + (37901/70)*n + 143 for n>5.
Conjectures from Colin Barker, Aug 26 2018: (Start)
G.f.: x*(128 - 37*x - 1893*x^2 + 5276*x^3 - 5539*x^4 + 1495*x^5 + 1526*x^6 - 1101*x^7 + 65*x^8 + 155*x^9 - 160*x^10 + 117*x^11 - 31*x^12) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>13.
(End)
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