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 12 results. Next

A267913 Number of 2 X n 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

2, 14, 96, 726, 5046, 35574, 242406, 1653750, 11113926, 74553750, 496532454, 3300259254, 21854907654, 144501754326, 953526151206, 6285325782006, 41384363469126, 272296902013974, 1790471038255206, 11767947840324150
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Row 2 of A267911.

Examples

			Some solutions for n=6:
..0..1..0..2..1..1....0..1..0..2..1..2....0..0..1..1..2..2....0..0..1..0..1..2
..1..1..2..1..2..1....2..2..0..2..1..2....2..1..1..0..0..2....1..0..0..1..2..2

Links

Crossrefs

Cf. A267911.

Formula

Empirical: a(n) = 11*a(n-1) - 2*a(n-2) - 288*a(n-3) + 544*a(n-4) + 1792*a(n-5) - 4096*a(n-6) for n>8.
Empirical g.f.: 2*x*(1 - 4*x - 27*x^2 + 137*x^3 + 98*x^4 - 1016*x^5 + 576*x^6 + 1024*x^7) / ((1 - 4*x)*(1 + 4*x)*(1 - 9*x + 16*x^2)*(1 - 2*x - 16*x^2)). - Colin Barker, Feb 21 2018

A267906 Number of n X 2 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

2, 14, 122, 938, 6734, 45938, 302402, 1939154, 12192302, 75508538, 462161714, 2802600938, 16870221902, 100950439394, 601202522882, 3566576610338, 21091803794894, 124410954720938, 732300042558002, 4302980995610234
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Column 2 of A267911.

Examples

			Some solutions for n=6:
..0..1....0..1....0..1....0..1....0..0....0..1....0..1....0..0....0..1....0..1
..0..2....2..2....1..1....0..0....1..1....1..0....2..0....1..2....2..2....2..2
..1..0....1..0....1..1....2..2....0..0....2..0....2..1....2..0....2..0....0..1
..2..1....0..0....0..2....1..1....1..1....2..0....2..2....1..0....1..2....1..2
..0..1....2..0....2..1....2..0....2..0....1..2....0..0....0..2....2..2....1..1
..0..1....0..2....1..1....1..2....0..1....2..1....2..2....1..0....2..1....0..1

Links

Crossrefs

Cf. A267911.

Formula

Empirical: a(n) = 14*a(n-1) - 60*a(n-2) + 50*a(n-3) + 145*a(n-4) - 80*a(n-5) - 84*a(n-6) + 16*a(n-7).
Empirical g.f.: 2*x*(1 - 7*x + 23*x^2 - 15*x^3 - 34*x^4 - 14*x^5 + 4*x^6) / ((1 - x)*(1 + x)*(1 - 4*x)*(1 - 6*x + x^2)*(1 - 4*x - 4*x^2)). - Colin Barker, Feb 25 2018

A267912 Number of 1 X n 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

1, 2, 4, 11, 29, 77, 201, 525, 1361, 3525, 9097, 23453, 60353, 155189, 398649, 1023501, 2626289, 6736677, 17274601, 44286845, 113516321, 290925845, 745515417, 1910267373, 4894426193, 12539689989, 32125783369, 82301320541, 210838008449
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Row 1 of A267911.

Examples

			Some solutions for n=8:
..0..1..1..2..0..1..2..0....0..1..2..0..2..0..1..0....0..1..2..0..0..1..0..2

Links

Crossrefs

Cf. A267911.

Formula

Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - 8*a(n-3) for n>5.
Conjectures from Colin Barker, Feb 25 2018: (Start)
G.f.: x*(1 - x - 4*x^2 + 3*x^3 + 4*x^4) / ((1 - 2*x)*(1 - x - 4*x^2)).
a(n) = (1/17)*2^(-5-n)*(-17*4^(1+n) + (85-19*sqrt(17))*(1-sqrt(17))^n + (1+sqrt(17))^n*(85+19*sqrt(17))) for n>2.
(End)

A267905 Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

1, 2, 5, 13, 34, 88, 225, 569, 1426, 3548, 8777, 21613, 53026, 129712, 316545, 770993, 1874914, 4553588, 11047625, 26779909, 64869586, 157043368, 380004897, 919150313, 2222499826, 5372538572, 12984354185, 31374801373, 75801065794
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Examples

			Some solutions for n=8:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....1....1....1....1....1....1....1....1....1....1....1....1....1....0
..1....2....2....0....2....2....2....1....2....0....2....0....2....0....2....0
..2....2....2....0....1....1....1....1....0....1....0....1....1....0....0....1
..0....1....2....2....2....1....2....2....0....1....0....2....0....0....0....2
..1....0....2....0....1....1....1....1....1....1....0....0....2....2....0....1
..2....2....2....0....2....1....2....0....0....0....1....1....2....0....0....0
..1....2....2....1....1....1....2....2....2....1....0....1....2....0....2....0

Links

Crossrefs

Column 1 of A267911.

Formula

Empirical: a(n) = 5*a(n-1) -7*a(n-2) +a(n-3) +2*a(n-4).
Conjectures from Colin Barker, Jan 11 2019: (Start)
G.f.: x*(1 - 3*x + 2*x^2 + x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)).
a(n) = ((1-sqrt(2))^(1+n) + (1+sqrt(2))^(1+n) - 2*(2^n-1)) / 4.
(End)

A267907 Number of nX3 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

4, 96, 2304, 43972, 754852, 12017350, 181535822, 2638824216, 37263580006, 514648921140, 6985835894832, 93540620739538, 1238999184320608, 16269402566811754, 212148448282604414, 2750808905345217294
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Column 3 of A267911.

Examples

			Some solutions for n=4
..0..1..1....0..0..1....0..1..2....0..1..1....0..0..1....0..1..2....0..1..2
..2..2..1....2..1..1....2..1..2....1..0..0....0..0..1....1..0..0....0..1..1
..1..0..2....2..1..0....1..0..2....2..0..1....0..1..1....1..2..0....0..0..2
..2..0..1....0..2..1....2..1..0....0..0..2....0..0..2....2..1..0....0..2..2

Links

Crossrefs

Cf. A267911.

Formula

Empirical recurrence of order 54 (see link above)

A267908 Number of nX4 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

11, 726, 47916, 2331981, 98614986, 3774659262, 134786758099, 4574297266940, 149403639631334, 4738376096688749, 146873341033699972, 4471066919904073296, 134165935575637438787, 3980005021518381534082, 116980704393934615092268
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Column 4 of A267911.

Examples

			Some solutions for n=3
..0..1..1..0....0..0..1..1....0..1..2..1....0..1..2..1....0..1..2..1
..1..1..2..2....1..0..1..2....1..2..0..0....2..0..0..1....1..0..2..0
..2..1..1..2....1..1..2..2....1..0..1..1....1..2..0..1....2..0..2..2

Links

Crossrefs

Cf. A267911.

A267909 Number of nX5 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

29, 5046, 878004, 104491831, 10441322974, 922017784240, 74691010105571, 5680483902454184, 411946383314752314, 28803298484312712803, 1957402980977660239136, 130069621243447882741372
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Column 5 of A267911.

Examples

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

Links

Crossrefs

Cf. A267911.

A267914 Number of 3Xn 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

5, 122, 2304, 47916, 878004, 16435188, 292341636, 5209312500, 90756319716, 1576811812500, 27101734404228, 464405881704372, 7914055449851172, 134550496512585684, 2280733479912724164, 38598223339253538036
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Row 3 of A267911.

Examples

			Some solutions for n=4
..0..1..2..2....0..0..1..1....0..1..2..1....0..1..0..2....0..0..1..2
..2..0..2..2....0..2..1..0....2..0..0..2....1..1..2..2....2..2..0..0
..0..0..1..1....0..0..2..0....2..2..0..0....1..2..2..1....2..1..2..1

Links

Crossrefs

Cf. A267911.

Formula

Empirical: a(n) = 31*a(n-1) -26*a(n-2) -6768*a(n-3) +39456*a(n-4) +479232*a(n-5) -3704832*a(n-6) -12386304*a(n-7) +115867648*a(n-8) +83886080*a(n-9) -1073741824*a(n-10) for n>12

A267915 Number of 4Xn 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

13, 938, 43972, 2331981, 104491831, 4817531571, 207508204575, 8960112001163, 375426257575299, 15673406360156331, 644971612069289479, 26434347183210422659, 1075438596218448452443, 43616300555346348016639
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Row 4 of A267911.

Examples

			Some solutions for n=3
..0..0..1....0..1..0....0..0..1....0..1..0....0..1..0....0..1..2....0..1..2
..1..2..0....0..2..0....2..1..2....0..0..1....0..2..0....2..2..1....2..0..0
..0..2..2....1..1..0....0..2..1....2..0..2....0..0..2....0..1..2....1..0..0
..0..1..0....2..2..1....0..1..2....1..0..2....2..1..1....0..1..0....2..1..1

Links

Crossrefs

Cf. A267911.

A267916 Number of 5Xn 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.

Original entry on oeis.org

34, 6734, 754852, 98614986, 10441322974, 1145682971200, 115481667816142, 11676922629038734, 1137131204736014484, 110241494900681903644, 10496364364121629281022, 994376596006517401565186
Offset: 1

Views

Author

R. H. Hardin, Jan 22 2016

Keywords

Comments

Row 5 of A267911.

Examples

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

Links

Crossrefs

Cf. A267911.
Showing 1-10 of 12 results. Next

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