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.

A243599 Number of length n+2 0..n arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..n introduced in 0..n order.

Original entry on oeis.org

3, 9, 28, 96, 365, 1533, 7049, 35166, 188834, 1084179, 6618471, 42756207, 291120550, 2081922514, 15590248867, 121920095673, 993343650911, 8414029179364, 73953763887276, 673316834487161, 6340176007793059, 61657373569634585
Offset: 1

Views

Author

R. H. Hardin, Jun 07 2014

Keywords

Comments

Diagonal of A243607.

Examples

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

Links

Crossrefs

Cf. A243607.

A243600 Number of length n+2 0..3 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..3 introduced in 0..3 order.

Original entry on oeis.org

4, 10, 28, 85, 269, 870, 2844, 9346, 30792, 101577, 335289, 1107066, 3655876, 12073706, 39875396, 131697309, 434963141, 1436579966, 4744692092, 15670638530, 51756579024, 170940329233, 564577491697, 1864672682930, 6158595344068
Offset: 1

Views

Author

R. H. Hardin, Jun 07 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....0....1....0....0....1....1....1....0....0....0....1....1....1....1....1
..2....1....2....0....1....2....2....2....1....1....0....2....2....1....1....2
..3....2....2....1....2....0....3....3....2....1....0....3....3....2....2....2
..3....2....1....1....2....3....1....3....0....2....1....0....3....3....2....0
..1....3....0....1....2....3....0....3....3....3....1....0....3....0....0....0
..2....0....3....0....0....2....2....1....1....1....2....1....3....1....1....2

Links

Crossrefs

Column 3 of A243607.

Formula

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

A243601 Number of length n+2 0..4 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..4 introduced in 0..4 order.

Original entry on oeis.org

4, 10, 29, 96, 349, 1350, 5425, 22297, 92841, 389456, 1640630, 6927937, 29294645, 123967625, 524830618, 2222483751, 9412820990, 39869076285, 168877805414, 715352976032, 3030223762722, 12836088840031, 54374194848619
Offset: 1

Views

Author

R. H. Hardin, Jun 07 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....1....1....1....1....1....1....1....1....1....1....1....1
..1....2....1....2....2....1....1....2....1....2....2....2....2....2....2....2
..1....3....1....3....3....2....2....0....0....3....3....3....3....3....3....2
..2....1....0....3....1....2....3....3....2....1....1....1....0....3....0....3
..3....2....2....0....2....1....0....3....3....1....4....4....0....3....1....3
..1....3....2....2....4....3....2....3....4....1....2....4....2....4....3....2

Links

Crossrefs

Column 4 of A243607.

Formula

Empirical: a(n) = 8*a(n-1) - 18*a(n-2) + 5*a(n-3) + 17*a(n-4) - 4*a(n-5) - 6*a(n-6) - a(n-7).
Empirical g.f.: x*(4 - 22*x + 21*x^2 + 24*x^3 - 15*x^4 - 13*x^5 - 2*x^6) / ((1 - x)*(1 - x - x^2)*(1 - 2*x - x^2)*(1 - 4*x - x^2)). - Colin Barker, Nov 02 2018

A243602 Number of length n+2 0..5 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..5 introduced in 0..5 order.

Original entry on oeis.org

4, 10, 29, 97, 365, 1511, 6726, 31544, 153328, 763187, 3857651, 19692114, 101153422, 521664456, 2697067469, 13966320059, 72395025823, 375501794607, 1948456098176, 10113010271486, 52497770870256, 272549948856853, 1415076190551061
Offset: 1

Views

Author

R. H. Hardin, Jun 07 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....0....1....1....0....1....0....1....1....1....1....1
..1....2....1....1....2....0....2....1....1....1....1....1....2....1....2....2
..1....2....2....2....0....1....3....0....1....2....2....1....0....0....3....2
..1....3....0....3....0....2....4....2....2....0....2....1....1....2....1....2
..2....3....3....4....0....2....4....1....3....3....3....0....1....2....1....0
..2....1....2....2....2....2....1....3....1....1....0....0....0....2....1....3

Links

Crossrefs

Column 5 of A243607.

Formula

Empirical: a(n) = 12*a(n-1) - 48*a(n-2) + 65*a(n-3) + 18*a(n-4) - 74*a(n-5) - 9*a(n-6) + 26*a(n-7) + 10*a(n-8) + a(n-9).
Empirical g.f.: x*(4 - 38*x + 101*x^2 - 31*x^3 - 129*x^4 + 18*x^5 + 63*x^6 + 21*x^7 + 2*x^8) / ((1 - x)*(1 - x - x^2)*(1 - 2*x - x^2)*(1 - 3*x - x^2)*(1 - 5*x - x^2)). - Colin Barker, Nov 02 2018

A243603 Number of length n+2 0..6 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..6 introduced in 0..6 order.

Original entry on oeis.org

4, 10, 29, 97, 366, 1533, 7020, 34631, 181391, 995139, 5651157, 32902123, 194971159, 1169639664, 7076433285, 43062727014, 263096669677, 1611790269519, 9892521309824, 60793268309048, 373921041602730, 2301237378396793
Offset: 1

Views

Author

R. H. Hardin, Jun 07 2014

Keywords

Comments

Column 6 of A243607

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....0....1....1....1....1....1....1....1....1....1....0....1....0
..2....2....2....1....2....2....2....2....1....2....1....2....1....1....2....1
..2....2....0....2....3....3....2....3....2....2....2....3....1....1....3....1
..2....0....0....3....0....0....1....1....3....3....0....4....2....2....3....2
..3....0....3....3....2....4....3....4....3....4....0....4....0....3....4....3
..3....0....4....4....2....5....3....4....2....0....2....1....1....4....5....1

Links

Formula

Empirical: a(n) = 17*a(n-1) -106*a(n-2) +286*a(n-3) -245*a(n-4) -231*a(n-5) +329*a(n-6) +147*a(n-7) -106*a(n-8) -74*a(n-9) -15*a(n-10) -a(n-11)

A243604 Number of length n+2 0..7 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..7 introduced in 0..7 order.

Original entry on oeis.org

4, 10, 29, 97, 366, 1534, 7049, 35129, 187993, 1069914, 6413136, 40104257, 259358085, 1721368017, 11650893890, 80015045418, 555433766065, 3885803906493, 27339242339942, 193138394368496, 1368463903086546, 9716805805575427
Offset: 1

Views

Author

R. H. Hardin, Jun 07 2014

Keywords

Comments

Column 7 of A243607

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....0....1....0....1....1....0....1....1....1....1....1....0....1
..2....2....2....1....1....0....2....2....1....2....2....2....2....1....1....2
..3....0....2....2....2....0....3....2....2....3....3....0....2....2....2....3
..3....1....0....2....2....1....0....3....2....1....1....0....3....3....0....1
..3....2....1....3....1....1....2....1....1....0....4....0....1....0....1....0
..4....0....2....3....1....1....2....4....1....4....2....2....1....1....2....2

Links

Formula

Empirical: a(n) = 23*a(n-1) -206*a(n-2) +894*a(n-3) -1814*a(n-4) +902*a(n-5) +1940*a(n-6) -1536*a(n-7) -1306*a(n-8) +394*a(n-9) +526*a(n-10) +162*a(n-11) +21*a(n-12) +a(n-13)

A243605 Number of length n+2 0..8 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..8 introduced in 0..8 order.

Original entry on oeis.org

4, 10, 29, 97, 366, 1534, 7050, 35166, 188788, 1082913, 6592698, 42315731, 284431573, 1988554321, 14365186163, 106571030511, 807548257486, 6221612919342, 48551842571129, 382621726260959, 3037888284516885
Offset: 1

Views

Author

R. H. Hardin, Jun 07 2014

Keywords

Comments

Column 8 of A243607

Examples

			Some solutions for n=5
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....1....0....1....1....0....1....1....1....1....0....1....0....1
..1....0....1....1....1....2....2....0....2....2....2....2....1....2....1....1
..1....1....2....2....1....0....0....1....3....2....3....2....2....3....1....2
..1....2....3....3....0....1....0....1....1....3....4....1....0....4....1....0
..2....3....1....4....2....3....3....1....0....4....5....3....0....0....0....1
..2....0....1....0....3....4....3....2....4....5....6....3....3....0....0....2

Links

Formula

Empirical: a(n) = 30*a(n-1) -365*a(n-2) +2297*a(n-3) -7771*a(n-4) +12461*a(n-5) -2366*a(n-6) -15807*a(n-7) +7237*a(n-8) +10936*a(n-9) -841*a(n-10) -3849*a(n-11) -1625*a(n-12) -307*a(n-13) -28*a(n-14) -a(n-15)

A243606 Number of length n+2 0..9 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..9 introduced in 0..9 order.

Original entry on oeis.org

4, 10, 29, 97, 366, 1534, 7050, 35167, 188834, 1084123, 6616633, 42711918, 290232665, 2066233824, 15337289086, 118111928594, 938944428249, 7667833845713, 64035036092080, 544629289107076, 4700922875545352
Offset: 1

Views

Author

R. H. Hardin, Jun 07 2014

Keywords

Comments

Column 9 of A243607

Examples

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

Links

Formula

Empirical: a(n) = 38*a(n-1) -603*a(n-2) +5165*a(n-3) -25592*a(n-4) +71533*a(n-5) -92714*a(n-6) -10048*a(n-7) +134330*a(n-8) -29886*a(n-9) -94396*a(n-10) -8366*a(n-11) +29547*a(n-12) +16394*a(n-13) +4033*a(n-14) +529*a(n-15) +36*a(n-16) +a(n-17)
Showing 1-8 of 8 results.

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