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 1-7 of 7 results.

A243634 Number of length n+2 0..n arrays with no three unequal elements in a row and new values 0..n introduced in 0..n order.

Original entry on oeis.org

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16737, 46905, 133556, 386062, 1132107, 3365627, 10137559, 30920943, 95457178, 298128278, 941574417, 3006040523, 9697677885, 31602993021, 104001763258, 345524136076, 1158570129917
Offset: 1

Views

Author

R. H. Hardin, Jun 08 2014

Keywords

Comments

Diagonal of A243641.

Examples

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

Links

Crossrefs

Cf. A247100.

A243635 Number of length n+2 0..4 arrays with no three unequal elements in a row and new values 0..4 introduced in 0..4 order.

Original entry on oeis.org

4, 9, 21, 51, 127, 324, 844, 2242, 6062, 16655, 46411, 130937, 373349, 1074194, 3114146, 9085176, 26643492, 78470989, 231925649, 687430207, 2042284587, 6078844480, 18121207896, 54086361422, 161592030394, 483170313579
Offset: 1

Views

Author

R. H. Hardin, Jun 08 2014

Keywords

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....1....0....1....0....0....0....1....0....1....1....1....0....0....1....1
..1....1....1....1....1....0....1....1....1....1....0....0....1....1....0....1
..0....0....1....1....1....0....0....1....0....1....0....1....0....1....1....2
..1....1....1....1....2....1....0....2....0....0....2....0....0....2....0....1
..0....1....2....2....2....1....1....2....1....0....2....0....2....2....0....1
..0....1....1....2....1....1....1....0....1....0....0....0....2....0....0....0
..2....1....2....3....2....2....0....0....1....0....0....1....2....0....0....0

Links

Crossrefs

Column 4 of A243641.

Formula

Empirical: a(n) = 7*a(n-1) - 14*a(n-2) + 21*a(n-4) - 7*a(n-5) - 6*a(n-6).
Empirical g.f.: x*(4 - 19*x + 14*x^2 + 30*x^3 - 20*x^4 - 12*x^5) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)). - Colin Barker, Nov 02 2018

A243636 Number of length n+2 0..5 arrays with no three unequal elements in a row and new values 0..5 introduced in 0..5 order.

Original entry on oeis.org

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16736, 46892, 133443, 385277, 1127352, 3339464, 10003395, 30269129, 92422160, 284470820, 881804563, 2750412037, 8625112792, 27174303856, 85960269683, 272856760081, 868664396112
Offset: 1

Views

Author

R. H. Hardin, Jun 08 2014

Keywords

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....0....1....0....1....1....1....1....0....0....1....0....0....0....0....1
..1....0....1....0....1....0....0....1....1....1....1....0....0....1....1....1
..1....0....2....1....1....1....0....2....1....0....1....1....1....1....0....0
..0....0....2....1....2....1....1....1....2....0....1....1....1....2....1....1
..1....0....0....1....2....0....1....2....2....2....1....2....0....2....1....0
..1....1....0....1....2....1....0....2....2....2....0....2....0....3....0....0
..1....1....1....1....3....1....1....2....3....0....1....1....0....2....1....2

Links

Crossrefs

Column 5 of A243641.

Formula

Empirical: a(n) = 9*a(n-1) - 25*a(n-2) + 7*a(n-3) + 64*a(n-4) - 54*a(n-5) - 48*a(n-6) + 32*a(n-7) + 16*a(n-8).
Empirical g.f.: x*(4 - 27*x + 40*x^2 + 59*x^3 - 126*x^4 - 51*x^5 + 80*x^6 + 32*x^7) / ((1 - x)*(1 - 2*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 4*x^2)). - Colin Barker, Nov 02 2018

A243637 Number of length n+2 0..6 arrays with no three unequal elements in a row and new values 0..6 introduced in 0..6 order.

Original entry on oeis.org

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16737, 46905, 133555, 386047, 1131958, 3364454, 10129563, 30871733, 95176427, 296618011, 933821451, 2967726939, 9514201392, 30747183016, 100097739315, 328049191105, 1081610514581
Offset: 1

Views

Author

R. H. Hardin, Jun 08 2014

Keywords

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....0....1....1....0....0....0....1....1....1....1....1....1....1....1
..1....0....1....1....1....1....0....1....1....1....1....0....0....1....1....1
..2....0....1....0....1....0....1....1....1....1....2....0....1....2....0....0
..1....1....1....0....0....0....1....0....2....2....2....1....1....2....0....1
..2....1....1....0....1....1....2....1....2....2....2....0....0....2....2....1
..2....2....2....0....0....0....2....0....1....2....3....0....0....1....0....1
..1....2....2....1....0....0....0....0....1....1....2....2....2....2....0....2

Links

Crossrefs

Column 6 of A243641.

Formula

Empirical: a(n) = 11*a(n-1) - 39*a(n-2) + 21*a(n-3) + 151*a(n-4) - 217*a(n-5) - 181*a(n-6) + 339*a(n-7) + 130*a(n-8) - 154*a(n-9) - 60*a(n-10).
Empirical g.f.: x*(4 - 35*x + 78*x^2 + 87*x^3 - 408*x^4 - 16*x^5 + 668*x^6 + 57*x^7 - 368*x^8 - 120*x^9) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 5*x^2)). - Colin Barker, Nov 02 2018

A243638 Number of length n+2 0..7 arrays with no three unequal elements in a row and new values 0..7 introduced in 0..7 order.

Original entry on oeis.org

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16737, 46905, 133556, 386062, 1132106, 3365610, 10137369, 30919271, 95444507, 298042003, 941032182, 3002839544, 9679707876, 31506186516, 103497873819, 342976360273, 1146003129573
Offset: 1

Views

Author

R. H. Hardin, Jun 08 2014

Keywords

Examples

			Some solutions for n=6:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..0....0....0....0....1....0....0....1....1....1....1....0....1....0....1....0
..1....1....0....1....1....1....1....1....1....1....1....1....1....1....1....1
..0....0....1....1....0....1....1....2....1....0....0....0....2....0....2....0
..1....1....0....1....0....2....1....2....2....0....0....0....2....0....2....1
..0....1....1....1....1....1....0....0....2....1....2....1....2....0....0....0
..0....1....1....2....0....1....1....0....3....0....0....1....2....0....2....0
..0....0....1....1....1....1....0....3....3....0....0....2....2....0....0....1

Links

Crossrefs

Column 7 of A243641.

Formula

Empirical: a(n) = 13*a(n-1) - 56*a(n-2) + 44*a(n-3) + 305*a(n-4) - 633*a(n-5) - 476*a(n-6) + 1772*a(n-7) + 308*a(n-8) - 2060*a(n-9) - 368*a(n-10) + 864*a(n-11) + 288*a(n-12).
Empirical g.f.: x*(4 - 43*x + 128*x^2 + 106*x^3 - 976*x^4 + 392*x^5 + 2696*x^6 - 1239*x^7 - 3714*x^8 + 363*x^9 + 2016*x^10 + 576*x^11) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - 3*x)*(1 - 2*x - x^2)*(1 - 2*x - 2*x^2)*(1 - 2*x - 4*x^2)*(1 - 2*x - 6*x^2)). - Colin Barker, Nov 02 2018

A243639 Number of length n+2 0..8 arrays with no three unequal elements in a row and new values 0..8 introduced in 0..8 order.

Original entry on oeis.org

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16737, 46905, 133556, 386062, 1132107, 3365627, 10137558, 30920924, 95456942, 298125982, 941555265, 3005897555, 9696696210, 31596681866, 103963289341, 345299662267, 1157307776719
Offset: 1

Views

Author

R. H. Hardin, Jun 08 2014

Keywords

Comments

Column 8 of A243641

Examples

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

Links

Formula

Empirical: a(n) = 15*a(n-1) -76*a(n-2) +78*a(n-3) +554*a(n-4) -1518*a(n-5) -1000*a(n-6) +6492*a(n-7) -505*a(n-8) -13105*a(n-9) +2036*a(n-10) +13670*a(n-11) +672*a(n-12) -5632*a(n-13) -1680*a(n-14)

A243640 Number of length n+2 0..9 arrays with no three unequal elements in a row and new values 0..9 introduced in 0..9 order.

Original entry on oeis.org

4, 9, 21, 51, 127, 324, 844, 2243, 6073, 16737, 46905, 133556, 386062, 1132107, 3365627, 10137559, 30920943, 95457177, 298128257, 941574130, 3006037464, 9697650031, 31602766791, 104000078093, 345512414521, 1158493006765
Offset: 1

Views

Author

R. H. Hardin, Jun 08 2014

Keywords

Comments

Column 9 of A243641

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

Links

Formula

Empirical: a(n) = 17*a(n-1) -99*a(n-2) +125*a(n-3) +931*a(n-4) -3185*a(n-5) -1785*a(n-6) +19063*a(n-7) -6754*a(n-8) -56936*a(n-9) +32132*a(n-10) +99764*a(n-11) -41096*a(n-12) -100896*a(n-13) +5152*a(n-14) +42048*a(n-15) +11520*a(n-16)
Showing 1-7 of 7 results.

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