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 13 results. Next

A246473 Number of length n+3 0..2 arrays with no pair in any consecutive four terms totalling exactly 2.

Original entry on oeis.org

10, 14, 20, 28, 38, 52, 72, 100, 138, 190, 262, 362, 500, 690, 952, 1314, 1814, 2504, 3456, 4770, 6584, 9088, 12544, 17314, 23898, 32986, 45530, 62844, 86742, 119728, 165258, 228102, 314844, 434572, 599830, 827932, 1142776, 1577348, 2177178
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Comments

Column 2 of A246479.

Examples

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

Links

Crossrefs

Cf. A246479.

Formula

Empirical: a(n) = a(n-1) + a(n-4).
Empirical g.f.: 2*x*(5 + 2*x + 3*x^2 + 4*x^3) / (1 - x - x^4). - Colin Barker, Mar 19 2018

A246474 Number of length n+3 0..3 arrays with no pair in any consecutive four terms totalling exactly 3.

Original entry on oeis.org

60, 132, 292, 644, 1420, 3132, 6908, 15236, 33604, 74116, 163468, 360540, 795196, 1753860, 3868260, 8531716, 18817292, 41502844, 91537404, 201892100, 445287044, 982111492, 2166115084, 4777517212, 10537145916, 23240406916, 51258331044
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 3 of A246479.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-3).
Empirical g.f.: 4*x*(15 + 3*x + 7*x^2) / (1 - 2*x - x^3). - Colin Barker, Nov 06 2018

A246475 Number of length n+3 0..4 arrays with no pair in any consecutive four terms totalling exactly 4.

Original entry on oeis.org

172, 484, 1376, 3904, 11020, 31104, 87888, 248568, 702724, 1985932, 5612156, 15862556, 44837136, 126731180, 358188232, 1012377900, 2861418780, 8087637712, 22859103016, 64609341900, 182613147216, 516142417472, 1458837964296
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 4 of A246479.

Formula

Empirical: a(n) = 2*a(n-1) + a(n-3) + 14*a(n-4) + 3*a(n-5) + 6*a(n-6) + a(n-8) + a(n-9).
Empirical g.f.: 4*x*(43 + 35*x + 102*x^2 + 245*x^3 + 80*x^4 + 99*x^5 + 7*x^6 + 21*x^7 + 16*x^8) / (1 - 2*x - x^3 - 14*x^4 - 3*x^5 - 6*x^6 - x^8 - x^9). - Colin Barker, Nov 06 2018

A246476 Number of length n+3 0..5 arrays with no pair in any consecutive four terms totalling exactly 5.

Original entry on oeis.org

462, 1734, 6534, 24582, 92478, 347934, 1309038, 4924998, 18529350, 69713094, 262282014, 986785278, 3712588494, 13967895174, 52551500358, 197714842182, 743863801278, 2798643484446, 10529354082798, 39614655463302
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Examples

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

Links

Crossrefs

Column 5 of A246479.

Formula

Empirical: a(n) = 3*a(n-1) + 2*a(n-2) + 3*a(n-3) +a(n-4).
Empirical g.f.: 6*x*(77 + 58*x + 68*x^2 + 21*x^3) / (1 - 3*x - 2*x^2 - 3*x^3 - x^4). - Colin Barker, Nov 06 2018

A246477 Number of length n+3 0..6 arrays with no pair in any consecutive four terms totaling exactly 6.

Original entry on oeis.org

966, 4386, 20004, 91212, 415650, 1893780, 8628792, 39320988, 179184654, 816514170, 3720653346, 16954232310, 77257406100, 352048294158, 1604217270528, 7310107829838, 33310766859666, 151790888076216, 691682436483000
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Comments

Column 6 of A246479.

Examples

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

Links

Crossrefs

Cf. A246479.

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) +3*a(n-3) +77*a(n-4) +55*a(n-5) +59*a(n-6) +18*a(n-7) +a(n-8) +4*a(n-9) +a(n-10).

A246478 Number of length n+3 0..7 arrays with no pair in any consecutive four terms totalling exactly 7.

Original entry on oeis.org

1880, 10376, 57416, 317576, 1756472, 9714968, 53733080, 297195272, 1643773832, 9091640072, 50285457464, 278126631896, 1538306048600, 8508302434184, 47059042885064, 260281476168584, 1439605284832568, 7962392893359512
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Examples

			Some solutions for n=3:
..5....0....1....0....2....4....6....0....2....5....6....7....2....7....7....7
..7....5....0....1....6....0....5....4....1....3....2....3....0....3....6....4
..5....6....1....4....7....1....6....1....7....1....6....6....3....3....4....7
..5....6....5....2....6....0....7....0....1....7....7....5....6....1....5....4
..5....0....0....2....2....2....6....0....5....7....6....5....5....2....4....7
..1....6....1....6....3....4....2....3....1....5....2....5....3....7....4....5

Links

Crossrefs

Column 7 of A246479.

Formula

Empirical: a(n) = 5*a(n-1) + 2*a(n-2) + 5*a(n-3) + a(n-4).
Empirical g.f.: 8*x*(235 + 122*x + 222*x^2 + 43*x^3) / (1 - 5*x - 2*x^2 - 5*x^3 - x^4). - Colin Barker, Nov 06 2018

A246480 Number of length 1+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

Original entry on oeis.org

2, 10, 60, 172, 462, 966, 1880, 3256, 5370, 8290, 12372, 17700, 24710, 33502, 44592, 58096, 74610, 94266, 117740, 145180, 177342, 214390, 257160, 305832, 361322, 423826, 494340, 573076, 661110, 758670, 866912, 986080, 1117410, 1261162
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 1 of A246479.

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) - 5*a(n-3) + 5*a(n-4) + a(n-5) - 3*a(n-6) + a(n-7).
Conjectures from Colin Barker, Nov 06 2018: (Start)
G.f.: 2*x*(1 + 2*x + 16*x^2 + 6*x^3 + 23*x^4) / ((1 - x)^5*(1 + x)^2).
a(n) = -n + 3*n^2 - 2*n^3 + n^4 for n even.
a(n) = -3 + 3*n + 3*n^2 - 2*n^3 + n^4 for n odd.
(End)

A246481 Number of length 2+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

Original entry on oeis.org

2, 14, 132, 484, 1734, 4386, 10376, 20840, 39690, 68950, 115212, 181644, 278222, 409514, 589584, 824656, 1133586, 1524510, 2021780, 2635700, 3396822, 4317874, 5436312, 6767544, 8356634, 10221926, 12416796, 14962780, 17922270, 21320250
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 2 of A246479.

Formula

Empirical: a(n) = 3*a(n-1) - 8*a(n-3) + 6*a(n-4) + 6*a(n-5) - 8*a(n-6) + 3*a(n-8) - a(n-9).
Conjectures from Colin Barker, Nov 06 2018: (Start)
G.f.: 2*x*(1 + 4*x + 45*x^2 + 52*x^3 + 191*x^4 + 72*x^5 + 115*x^6) / ((1 - x)^6*(1 + x)^3).
a(n) = 5*n - 11*n^2 + 10*n^3 - 4*n^4 + n^5 for n even.
a(n) = 9 - 10*n - 4*n^2 + 10*n^3 - 4*n^4 + n^5 for n odd.
(End)

A246482 Number of length 3+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

Original entry on oeis.org

2, 20, 292, 1376, 6534, 20004, 57416, 133664, 293770, 574100, 1073772, 1865280, 3134222, 5007716, 7797904, 11708864, 17227026, 24659604, 34722740, 47856800, 65070742, 86971940, 114932952, 149765856, 193285274, 246549524, 311901436
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Examples

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

Links

Crossrefs

Row 3 of A246479.

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - 11*a(n-3) + 6*a(n-4) + 14*a(n-5) - 14*a(n-6) - 6*a(n-7) + 11*a(n-8) - a(n-9) - 3*a(n-10) + a(n-11).
Conjectures from Colin Barker, Nov 06 2018: (Start)
G.f.: 2*x*(1 + 7*x + 115*x^2 + 251*x^3 + 1161*x^4 + 1045*x^5 + 2001*x^6 + 617*x^7 + 562*x^8) / ((1 - x)^7*(1 + x)^4).
a(n) = -20*n + 43*n^2 - 40*n^3 + 21*n^4 - 6*n^5 + n^6 for n even.
a(n) = -26 + 37*n + 5*n^2 - 30*n^3 + 21*n^4 - 6*n^5 + n^6 for n odd.
(End)

A246483 Number of length 4+3 0..n arrays with no pair in any consecutive four terms totalling exactly n.

Original entry on oeis.org

2, 28, 644, 3904, 24582, 91212, 317576, 857248, 2174090, 4780060, 10007052, 19154208, 35306894, 61236364, 103134992, 166247872, 261796626, 398879388, 596338580, 868942720, 1246516502, 1751814988, 2429877144, 3314320224
Offset: 1

Views

Author

R. H. Hardin, Aug 27 2014

Keywords

Comments

Row 4 of A246479

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) -14*a(n-3) +5*a(n-4) +25*a(n-5) -20*a(n-6) -20*a(n-7) +25*a(n-8) +5*a(n-9) -14*a(n-10) +2*a(n-11) +3*a(n-12) -a(n-13)
Showing 1-10 of 13 results. Next

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