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 1-5 of 5 results.

A242234 Number of length n+3+1 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+2 elements, and new values 0..3 introduced in order.

Original entry on oeis.org

10, 22, 43, 82, 157, 304, 586, 1129, 2176, 4195, 8086, 15586, 30043, 57910, 111625, 215164, 414742, 799441, 1540972, 2970319, 5725474, 11036206, 21272971, 41004970, 79039621, 152353768, 293671330, 566069689, 1091134408, 2103229195, 4054104622
Offset: 1

Views

Author

R. H. Hardin, May 08 2014

Keywords

Comments

Column 3 of A242239.

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

Links

Crossrefs

Cf. A016777, A145112, A242239.

Formula

Empirical: a(n) = a(n-1) +a(n-2) +a(n-3) +a(n-4).
Conjecture: a(n) = 9*A145112(n-1) + A016777(n-1). - R. J. Mathar, Aug 16 2017
Empirical g.f.: x*(10 + 12*x + 11*x^2 + 7*x^3) / (1 - x - x^2 - x^3 - x^4). - Colin Barker, Mar 19 2018

A242235 Number of length n+4+1 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+2 elements, and new values 0..4 introduced in order.

Original entry on oeis.org

15, 35, 71, 139, 271, 531, 1047, 2059, 4047, 7955, 15639, 30747, 60447, 118835, 233623, 459291, 902943, 1775139, 3489831, 6860827, 13488031, 26516771, 52130599, 102486059, 201482287, 396103747, 778719463, 1530922155, 3009713711
Offset: 1

Views

Author

R. H. Hardin, May 08 2014

Keywords

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

Links

Crossrefs

Cf. A004767, A145113, A242239.
Column 4 of A242239.

Formula

Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5).
Conjecture: a(n) = 16*A145113(n-1) + A004767(n-2), n > 1. - R. J. Mathar, Aug 16 2017
Empirical g.f.: x*(15 + 20*x + 21*x^2 + 18*x^3 + 11*x^4) / (1 - x - x^2 - x^3 - x^4 - x^5). - Colin Barker, Oct 31 2018

A242236 Number of length n+5+1 0..5 arrays with every value 0..5 appearing at least once in every consecutive 5+2 elements, and new values 0..5 introduced in order.

Original entry on oeis.org

21, 51, 106, 211, 416, 821, 1626, 3231, 6411, 12716, 25221, 50026, 99231, 196836, 390441, 774471, 1536226, 3047231, 6044436, 11989641, 23782446, 47174451, 93574431, 185612636, 368178041, 730311646, 1448633651, 2873484856, 5699795261
Offset: 1

Views

Author

R. H. Hardin, May 08 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....0....1....1....1....1....1....1....0....1....1....1....1....1
..2....0....0....1....2....2....2....2....2....2....1....2....2....2....0....2
..3....2....2....2....0....0....3....3....3....3....2....0....3....1....2....3
..2....3....3....3....3....3....4....0....4....4....3....3....3....3....3....4
..4....4....4....4....4....4....5....4....1....0....4....4....4....4....4....2
..5....5....5....5....5....5....1....5....5....5....5....5....5....5....5....5
..0....2....1....0....1....2....0....1....0....1....1....1....0....0....0....0
..1....1....0....2....2....1....3....3....2....2....0....0....1....4....1....1
..3....0....0....1....1....0....2....2....3....4....5....2....2....2....5....3
..3....3....2....4....0....5....1....0....2....3....2....5....3....1....2....5

Links

Crossrefs

Column 5 of A242239.

Formula

Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6).
Empirical g.f.: x*(21 + 30*x + 34*x^2 + 33*x^3 + 27*x^4 + 16*x^5) / (1 - x - x^2 - x^3 - x^4 - x^5 - x^6). - Colin Barker, Nov 01 2018

A242237 Number of length n+6+1 0..6 arrays with every value 0..6 appearing at least once in every consecutive 6+2 elements, and new values 0..6 introduced in order.

Original entry on oeis.org

28, 70, 148, 298, 592, 1174, 2332, 4642, 9256, 18442, 36736, 73174, 145756, 290338, 578344, 1152046, 2294836, 4571230, 9105724, 18138274, 36130792, 71971246, 143364148, 285576250, 568857664, 1133144098, 2257182472, 4496226670
Offset: 1

Views

Author

R. H. Hardin, May 08 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....1....1....1....1....1....1....1....0....1....1
..2....2....2....2....2....2....2....2....2....2....2....2....2....1....2....2
..3....3....0....3....3....3....0....3....3....3....3....3....3....2....3....3
..4....4....3....4....4....0....3....4....4....4....4....4....1....3....4....4
..0....1....4....5....0....4....4....5....0....5....5....5....4....4....5....5
..5....5....5....1....5....5....5....6....5....6....0....3....5....5....6....1
..6....6....6....6....6....6....6....0....6....0....6....6....6....6....1....6
..1....0....1....0....1....1....1....3....2....5....1....0....0....1....0....0
..3....2....0....3....2....2....0....1....1....1....2....1....5....0....2....2
..2....3....2....2....3....3....2....2....3....2....3....2....2....2....3....3
..3....4....4....3....0....1....5....6....5....3....5....3....3....1....4....6

Links

Crossrefs

Column 6 of A242239.

Formula

Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7).
Empirical g.f.: 2*x*(14 + 21*x + 25*x^2 + 26*x^3 + 24*x^4 + 19*x^5 + 11*x^6) / (1 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7). - Colin Barker, Nov 01 2018

A242238 Number of length n+7+1 0..7 arrays with every value 0..7 appearing at least once in every consecutive 7+2 elements, and new values 0..7 introduced in order.

Original entry on oeis.org

36, 92, 197, 400, 799, 1590, 3165, 6308, 12587, 25138, 50184, 100171, 199942, 399085, 796580, 1589995, 3173682, 6334777, 12644416, 25238648, 50377125, 100554308, 200709531, 400622482, 799654969, 1596136256, 3185937735, 6359231054
Offset: 1

Views

Author

R. H. Hardin, May 08 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....1....0....1....1....1....0....1....0....1....1
..2....2....2....2....2....2....2....1....1....2....2....1....2....1....2....2
..3....3....3....3....3....3....3....2....2....3....3....2....3....2....0....3
..4....4....4....1....4....1....4....3....3....4....0....3....0....3....3....4
..5....5....5....4....5....4....5....4....4....0....4....4....4....4....4....5
..0....6....0....5....6....5....6....5....5....5....5....5....5....5....5....6
..6....0....6....6....2....6....7....6....6....6....6....6....6....6....6....0
..7....7....7....7....7....7....0....7....7....7....7....7....7....7....7....7
..1....2....2....0....0....0....1....0....0....1....3....0....2....2....6....3
..2....1....1....2....1....3....1....1....2....2....1....2....1....0....1....1
..3....3....3....3....6....2....2....2....1....3....2....1....3....1....2....2
..4....2....5....3....3....2....3....2....2....5....5....6....1....6....0....4

Links

Crossrefs

Column 7 of A242239.

Formula

Empirical: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7) + a(n-8).
Empirical g.f.: x*(36 + 56*x + 69*x^2 + 75*x^3 + 74*x^4 + 66*x^5 + 51*x^6 + 29*x^7) / (1 - x - x^2 - x^3 - x^4 - x^5 - x^6 - x^7 - x^8). - Colin Barker, Nov 01 2018
Showing 1-5 of 5 results.

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