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.

A243513 Number of length n+2 0..4 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..4 introduced in 0..4 order.

Original entry on oeis.org

3, 5, 10, 24, 65, 187, 552, 1646, 4927, 14769, 44294, 132868, 398589, 1195751, 3587236, 10761690, 32285051, 96855133, 290565378, 871696112, 2615088313, 7845264915, 23535794720, 70607384134, 211822152375, 635466457097
Offset: 1

Views

Author

R. H. Hardin, Jun 05 2014

Keywords

Examples

			All solutions for n=3:
..0....0....0....0....0....0....0....0....0....0
..1....0....1....0....0....1....1....1....0....0
..2....0....2....1....0....2....2....2....0....1
..3....1....0....2....0....0....3....3....0....2
..0....2....1....3....1....3....1....4....0....0

Links

Crossrefs

Column 4 of A243519.

Formula

Empirical: a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).
Conjectures from Colin Barker, Nov 02 2018: (Start)
G.f.: x*(3 - 10*x + 6*x^2) / ((1 - x)^2*(1 - 3*x)).
a(n) = (7 + 3^n + 2*n) / 4.
(End)

A243514 Number of length n+2 0..5 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..5 introduced in 0..5 order.

Original entry on oeis.org

3, 5, 10, 25, 76, 263, 978, 3773, 14824, 58771, 234046, 934121, 3732372, 14921279, 59668714, 238642069, 954502720, 3817879787, 15271256982, 61084503617, 244336965868, 977345766295, 3909378870850, 15637507094765, 62550011601816
Offset: 1

Views

Author

R. H. Hardin, Jun 05 2014

Keywords

Examples

			All solutions for n=3:
..0....0....0....0....0....0....0....0....0....0
..1....0....0....0....1....1....1....1....0....0
..2....1....0....1....2....2....2....2....0....0
..0....2....1....2....3....3....3....0....0....0
..1....0....2....3....1....0....4....3....1....0

Links

Crossrefs

Column 5 of A243519.

Formula

Empirical: a(n) = 8*a(n-1) - 21*a(n-2) + 22*a(n-3) - 8*a(n-4).
Conjectures from Colin Barker, Nov 02 2018: (Start)
G.f.: x*(3 - 19*x + 33*x^2 - 16*x^3) / ((1 - x)^2*(1 - 2*x)*(1 - 4*x)).
a(n) = (26 + 9*2^n + 4^n + 6*n) / 18.
(End)

A243515 Number of length n+2 0..6 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..6 introduced in 0..6 order.

Original entry on oeis.org

3, 5, 10, 25, 77, 279, 1134, 4979, 22981, 109453, 531458, 2610933, 12917685, 64181627, 319695982, 1594859887, 7963472189, 39784944801, 198827606706, 993846943841, 4968361974493, 24839192686975, 124188113975630
Offset: 1

Views

Author

R. H. Hardin, Jun 05 2014

Keywords

Examples

			All solutions for n=3:
..0....0....0....0....0....0....0....0....0....0
..1....0....1....0....1....1....0....1....0....0
..2....1....2....0....2....2....0....2....1....0
..3....2....3....1....0....3....0....0....2....0
..1....0....0....2....3....4....1....1....3....0

Links

Crossrefs

Column 6 of A243519.

Formula

Empirical: a(n) = 12*a(n-1) - 52*a(n-2) + 102*a(n-3) - 91*a(n-4) + 30*a(n-5).
Conjectures from Colin Barker, Nov 02 2018: (Start)
G.f.: x*(3 - 31*x + 106*x^2 - 141*x^3 + 60*x^4) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 5*x)).
a(n) = (147 + 2^(5+n) + 4*3^(1+n) + 5^n + 36*n) / 96.
(End)

A243516 Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order.

Original entry on oeis.org

3, 5, 10, 25, 77, 280, 1156, 5267, 25915, 135214, 736706, 4139833, 23767897, 138468212, 814675840, 4824766303, 28699128503, 171207852154, 1023332115838, 6124430348357, 36684624841813, 219860794899520, 1318179574171580
Offset: 1

Views

Author

R. H. Hardin, Jun 05 2014

Keywords

Examples

			All solutions for n=3:
..0....0....0....0....0....0....0....0....0....0
..0....0....0....1....0....1....1....1....0....1
..1....0....0....2....1....2....2....2....0....2
..2....0....1....3....2....3....0....3....0....0
..3....1....2....0....0....4....3....1....0....1

Links

Crossrefs

Column 7 of A243519.

Formula

Empirical: a(n) = 17*a(n-1) - 111*a(n-2) + 355*a(n-3) - 584*a(n-4) + 468*a(n-5) - 144*a(n-6).
Conjectures from Colin Barker, Nov 02 2018: (Start)
G.f.: x*(3 - 46*x + 258*x^2 - 655*x^3 + 739*x^4 - 288*x^5) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 6*x)).
a(n) = (2722 + 675*2^n + 25*2^(1+2*n) + 50*3^(1+n) + 2^n*3^(1+n) + 660*n) / 1800.
(End)

A243517 Number of length n+2 0..8 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..8 introduced in 0..8 order.

Original entry on oeis.org

3, 5, 10, 25, 77, 280, 1157, 5296, 26406, 141585, 807064, 4837587, 30181075, 194210670, 1279159631, 8571132698, 58153599684, 398124806735, 2743173705258, 18987825983429, 131858977691833, 917797527716980, 6398758306106345
Offset: 1

Views

Author

R. H. Hardin, Jun 05 2014

Keywords

Examples

			Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....1....1....1....0....0....0....1....1....1....0....1....1....1
..2....2....2....2....2....2....1....0....0....2....2....2....0....2....2....2
..3....3....3....3....3....3....2....0....0....0....3....3....1....0....3....3
..4....1....0....0....0....0....3....0....0....3....4....1....2....3....1....4
..5....0....1....4....2....2....0....1....0....4....1....0....3....4....2....1
..0....4....3....5....1....4....4....2....0....2....3....2....4....0....3....5

Links

Crossrefs

Column 8 of A243519.

Formula

Empirical: a(n) = 23*a(n-1) - 212*a(n-2) + 1010*a(n-3) - 2669*a(n-4) + 3887*a(n-5) - 2878*a(n-6) + 840*a(n-7).
Empirical g.f.: x*(3 - 64*x + 531*x^2 - 2175*x^3 + 4579*x^4 - 4607*x^5 + 1680*x^6) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 7*x)). - Colin Barker, Nov 02 2018

A243518 Number of length n+2 0..9 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..9 introduced in 0..9 order.

Original entry on oeis.org

3, 5, 10, 25, 77, 280, 1157, 5297, 26443, 142372, 819731, 5009281, 32252381, 217194296, 1518771097, 10952508217, 80950970231, 609958242292, 4664758144295, 36080343085145, 281462510140633, 2209800140157400, 17432715938447165
Offset: 1

Views

Author

R. H. Hardin, Jun 05 2014

Keywords

Examples

			Some solutions for n=5:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....0....1....0....1....0....1....1....0....1....1....1....1
..2....2....1....2....0....2....0....2....1....2....2....1....2....2....2....2
..3....3....2....3....0....3....1....3....2....0....0....2....3....3....0....3
..4....0....3....4....1....0....2....1....3....3....3....0....1....0....3....1
..1....4....0....0....2....1....3....4....1....4....1....1....4....1....4....4
..2....2....1....2....3....3....1....3....4....1....4....2....0....2....5....5

Links

Crossrefs

Column 9 of A243519.

Formula

Empirical: a(n) = 30*a(n-1) - 372*a(n-2) + 2478*a(n-3) - 9639*a(n-4) + 22260*a(n-5) - 29588*a(n-6) + 20592*a(n-7) - 5760*a(n-8).
Empirical g.f.: x*(3 - 85*x + 976*x^2 - 5849*x^3 + 19574*x^4 - 36095*x^5 + 33305*x^6 - 11520*x^7) / ((1 - x)^2*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 8*x)). - Colin Barker, Nov 02 2018
Showing 1-6 of 6 results.

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