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 1-8 of 8 results.

A202195 Number of (n+2) X 3 binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

108, 240, 450, 756, 1176, 1728, 2430, 3300, 4356, 5616, 7098, 8820, 10800, 13056, 15606, 18468, 21660, 25200, 29106, 33396, 38088, 43200, 48750, 54756, 61236, 68208, 75690, 83700, 92256, 101376, 111078, 121380, 132300, 143856, 156066, 168948
Offset: 1

Views

Author

R. H. Hardin, Dec 14 2011

Keywords

Comments

Column 1 of A202202.

Examples

			Some solutions for n=10:
  0 0 0    0 0 0    1 0 0    1 0 0    1 0 0    0 1 1    0 1 1
  1 1 1    0 1 1    0 1 1    1 1 0    1 1 1    1 1 1    1 1 1
  1 1 0    0 1 1    0 1 1    0 1 0    1 1 1    1 1 1    1 1 1
  1 1 0    0 1 1    0 1 1    0 1 0    1 1 0    1 1 1    1 1 1
  1 1 0    0 1 1    0 1 0    0 1 0    1 0 0    1 1 1    1 1 1
  0 1 0    0 1 1    0 0 0    0 1 0    0 0 0    1 1 1    1 1 0
  0 1 0    0 1 1    0 0 0    0 1 0    0 0 0    1 1 0    1 0 0
  0 1 0    0 1 1    0 0 0    0 0 0    0 0 0    1 1 0    0 0 0
  0 1 0    0 1 0    0 0 0    0 0 0    0 0 0    0 1 0    0 0 0
  0 1 0    0 1 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 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. A202202.

Formula

Empirical: a(n) = 3*(n+3)*(n+2)^2 = 3*A011379(n+2).
Conjectures from Colin Barker, Mar 03 2018: (Start)
G.f.: 6*x*(18 - 32*x + 23*x^2 - 6*x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A202194 Number of (n+2)X(n+2) binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

108, 640, 3500, 18144, 90552, 439296, 2084940, 9724000, 44710952, 203164416, 914004728, 4077035200, 18052470000, 79420170240, 347424465420, 1512176830560, 6552247686600, 28276211040000, 121580638419240, 521033622457920
Offset: 1

Views

Author

R. H. Hardin Dec 14 2011

Keywords

Comments

Diagonal of A202202

Examples

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

Links

Programs

  • PARI
    {a(n) = if(n<1, 0, 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!))}; /* Michael Somos, Sep 11 2020 */

Formula

Empirical: (n+1)*a(n) -2*(3n+4)*a(n-1) +4*(3n-2)*a(n-2) +8*(3-2n)*a(n-3)=0. - R. J. Mathar, Dec 14 2011
Conjecture: a(n) = 4*(n+2)^2 * (2*n+1)!/(n! * (n+1)!). - Michael Somos, Sep 11 2020

A202196 Number of (n+2) X 4 binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

240, 640, 1400, 2688, 4704, 7680, 11880, 17600, 25168, 34944, 47320, 62720, 81600, 104448, 131784, 164160, 202160, 246400, 297528, 356224, 423200, 499200, 585000, 681408, 789264, 909440, 1042840, 1190400, 1353088, 1531904, 1727880, 1942080
Offset: 1

Views

Author

R. H. Hardin, Dec 14 2011

Keywords

Comments

Column 2 of A202202.

Examples

			Some solutions for n=6:
..0..1..1..1....1..1..1..1....1..1..1..0....1..1..1..1....1..1..1..1
..1..1..1..1....1..1..1..0....1..1..1..1....1..1..1..1....1..1..1..1
..1..1..1..1....1..1..0..0....1..1..1..0....0..1..1..1....1..1..1..1
..1..1..1..0....1..1..0..0....0..1..1..0....0..1..1..1....1..1..1..1
..1..1..1..0....1..1..0..0....0..1..1..0....0..1..1..1....1..1..1..1
..1..1..1..0....1..1..0..0....0..1..0..0....0..1..1..0....0..1..1..1
..1..1..0..0....1..1..0..0....0..0..0..0....0..1..1..0....0..1..1..0
..1..1..0..0....1..1..0..0....0..0..0..0....0..1..0..0....0..1..1..0

Links

Crossrefs

Cf. A202202.

Formula

Empirical: a(n) = 4*(n+4)*(n+3)*(n+2)^2/3.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: 8*x*(30 - 70*x + 75*x^2 - 39*x^3 + 8*x^4) / (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>5.
(End)

A202197 Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

450, 1400, 3500, 7560, 14700, 26400, 44550, 71500, 110110, 163800, 236600, 333200, 459000, 620160, 823650, 1077300, 1389850, 1771000, 2231460, 2783000, 3438500, 4212000, 5118750, 6175260, 7399350, 8810200, 10428400, 12276000, 14376560
Offset: 1

Views

Author

R. H. Hardin, Dec 14 2011

Keywords

Comments

Column 3 of A202202.

Examples

			Some solutions for n=4:
..1..1..1..0..0....1..1..1..0..0....0..0..0..0..0....0..1..0..0..0
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....1..1..1..1..0
..1..1..1..1..1....1..1..1..1..1....1..1..1..1..1....0..1..1..0..0
..0..1..0..0..0....0..1..1..1..1....0..1..1..0..0....0..1..1..0..0
..0..1..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..0....0..0..0..0..0....0..1..1..0..0

Links

Crossrefs

Cf. A202202.

Formula

Empirical: a(n) = 5*(n+5)*(n+4)*(n+3)*(n+2)^2/12.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: 10*x*(45 - 130*x + 185*x^2 - 144*x^3 + 59*x^4 - 10*x^5) / (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>6.
(End)

A202198 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

756, 2688, 7560, 18144, 38808, 76032, 138996, 240240, 396396, 628992, 965328, 1439424, 2093040, 2976768, 4151196, 5688144, 7671972, 10200960, 13388760, 17365920, 22281480, 28304640, 35626500, 44461872, 55051164, 67662336, 82592928
Offset: 1

Views

Author

R. H. Hardin, Dec 14 2011

Keywords

Comments

Column 4 of A202202.

Examples

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

Links

Crossrefs

Cf. A202202.

Formula

Empirical: a(n) = (n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/10.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: 12*x*(63 - 217*x + 385*x^2 - 399*x^3 + 245*x^4 - 83*x^5 + 12*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)

A202199 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

1176, 4704, 14700, 38808, 90552, 192192, 378378, 700700, 1233232, 2079168, 3378648, 5317872, 8139600, 12155136, 17757894, 25438644, 35802536, 49588000, 67687620, 91171080, 121310280, 159606720, 207821250, 268006284, 342540576
Offset: 1

Views

Author

R. H. Hardin, Dec 14 2011

Keywords

Comments

Column 5 of A202202.

Examples

			Some solutions for n=2:
..1..1..1..1..1..1..0....1..1..1..0..0..0..0....0..1..1..1..1..1..1
..1..1..1..1..1..0..0....1..1..1..1..1..1..1....1..1..1..1..1..0..0
..1..0..0..0..0..0..0....1..0..0..0..0..0..0....1..1..1..1..0..0..0
..1..0..0..0..0..0..0....0..0..0..0..0..0..0....1..0..0..0..0..0..0

Links

Crossrefs

Cf. A202202.

Formula

Empirical: a(n) = 7*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/360.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: 14*x*(84 - 336*x + 714*x^2 - 924*x^3 + 756*x^4 - 384*x^5 + 111*x^6 - 14*x^7) / (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>8.
(End)

A202200 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

1728, 7680, 26400, 76032, 192192, 439296, 926640, 1830400, 3422848, 6110208, 10480704, 17364480, 27907200, 43659264, 66682704, 99677952, 146132800, 210496000, 298378080, 416782080, 574367040, 781747200, 1051830000, 1400196096
Offset: 1

Views

Author

R. H. Hardin, Dec 14 2011

Keywords

Comments

Column 6 of A202202.

Examples

			Some solutions for n=2:
..1..1..1..1..1..1..1..0....0..1..1..1..1..1..1..1....0..1..1..1..0..0..0..0
..1..1..1..1..1..0..0..0....1..1..1..1..1..1..0..0....1..0..0..0..0..0..0..0
..1..1..1..1..0..0..0..0....0..1..1..1..1..0..0..0....1..0..0..0..0..0..0..0
..0..1..1..0..0..0..0..0....0..1..1..1..0..0..0..0....0..0..0..0..0..0..0..0

Links

Crossrefs

Cf. A202202.

Formula

Empirical: a(n) = (n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/315.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: 16*x*(108 - 492*x + 1218*x^2 - 1890*x^3 + 1932*x^4 - 1308*x^5 + 567*x^6 - 143*x^7 + 16*x^8) / (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>9.
(End)

A202201 Number of (n+2) X 9 binary arrays avoiding patterns 001 and 101 in rows and columns.

Original entry on oeis.org

2430, 11880, 44550, 138996, 378378, 926640, 2084940, 4375800, 8664084, 16325712, 29476980, 51279480, 86337900, 141210432, 225054126, 350430300, 534298050, 799227000, 1174863690, 1699689420, 2423110950, 3407929200, 4733235000
Offset: 1

Views

Author

R. H. Hardin, Dec 14 2011

Keywords

Comments

Column 7 of A202202.

Examples

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

Links

Crossrefs

Cf. A202202.

Formula

Empirical: a(n) = (n+9)*(n+8)*(n+7)*(n+6)*(n+5)*(n+4)*(n+3)*(n+2)^2/2240.
Conjectures from Colin Barker, May 27 2018: (Start)
G.f.: 18*x*(135 - 690*x + 1950*x^2 - 3528*x^3 + 4326*x^4 - 3660*x^5 + 2115*x^6 - 800*x^7 + 179*x^8 - 18*x^9) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10.
(End)
Showing 1-8 of 8 results.

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