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 1-4 of 4 results.

A202048 Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows and columns.

Original entry on oeis.org

636, 1968, 4980, 11016, 22092, 41088, 71964, 120000, 192060, 296880, 445380, 651000, 930060, 1302144, 1790508, 2422512, 3230076, 4250160, 5525268, 7103976, 9041484, 11400192, 14250300, 17670432, 21748284, 26581296, 32277348, 38955480
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2011

Keywords

Comments

Column 4 of A202052.

Examples

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

Links

Crossrefs

Cf. A202052.

Formula

Empirical: a(n) = (1/30)*n^6 + (9/10)*n^5 + (59/6)*n^4 + (111/2)*n^3 + (2552/15)*n^2 + (1278/5)*n + 144.
Conjectures from Colin Barker, May 25 2018: (Start)
G.f.: 12*x*(53 - 207*x + 380*x^2 - 398*x^3 + 245*x^4 - 83*x^5 + 12*x^6) / (1 - x)^7.
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)

A202049 Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows and columns.

Original entry on oeis.org

966, 3304, 9170, 22092, 47950, 95984, 180054, 320180, 544390, 890904, 1410682, 2170364, 3255630, 4775008, 6864158, 9690660, 13459334, 18418120, 24864546, 33152812, 43701518, 57002064, 73627750, 94243604, 119616966, 150628856
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2011

Keywords

Comments

Column 5 of A202052.

Examples

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

Links

Crossrefs

Cf. A202052.

Formula

Empirical: a(n) = (1/180)*n^7 + (7/36)*n^6 + (511/180)*n^5 + (805/36)*n^4 + (4606/45)*n^3 + (2443/9)*n^2 + (1854/5)*n + 196.
Conjectures from Colin Barker, May 26 2018: (Start)
G.f.: 14*x*(69 - 316*x + 699*x^2 - 918*x^3 + 755*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)

A202050 Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows and columns.

Original entry on oeis.org

1392, 5216, 15760, 41088, 95984, 205792, 411696, 777760, 1400080, 2418432, 4030832, 6511456, 10232400, 15689792, 23534800, 34610112, 49992496, 71042080, 99459024, 137348288, 187293232, 252438816, 336585200, 444292576, 580998096
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2011

Keywords

Comments

Column 6 of A202052.

Examples

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

Links

Crossrefs

Cf. A202052.

Formula

Empirical: a(n) = (1/1260)*n^8 + (11/315)*n^7 + (59/90)*n^6 + (308/45)*n^5 + (7807/180)*n^4 + (7667/45)*n^3 + (14139/35)*n^2 + (17876/35)*n + 256.
Conjectures from Colin Barker, May 26 2018: (Start)
G.f.: 16*x*(87 - 457*x + 1183*x^2 - 1869*x^3 + 1925*x^4 - 1307*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)

A202051 Number of (n+2) X 9 binary arrays avoiding patterns 001 and 110 in rows and columns.

Original entry on oeis.org

1926, 7848, 25650, 71964, 180054, 411696, 874998, 1750140, 3325410, 6046344, 10581246, 17906868, 29418570, 47069856, 73546794, 112483476, 168725358, 248648040, 360539802, 515057004, 725762286, 1009756368, 1388415150
Offset: 1

Views

Author

R. H. Hardin, Dec 10 2011

Keywords

Comments

Column 7 of A202052.

Examples

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

Links

Crossrefs

Cf. A202052.

Formula

Empirical: a(n) = (1/10080)*n^9 + (3/560)*n^8 + (211/1680)*n^7 + (67/40)*n^6 + (6709/480)*n^5 + (6041/80)*n^4 + (663941/2520)*n^3 + (79913/140)*n^2 + (4735/7)*n + 324.
Conjectures from Colin Barker, May 26 2018: (Start)
G.f.: 18*x*(107 - 634*x + 1880*x^2 - 3472*x^3 + 4298*x^4 - 3652*x^5 + 2114*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 1-4 of 4 results.

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