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.

A212833 Number of 0..n arrays of length n+1 with 0 never adjacent to n.

Original entry on oeis.org

2, 17, 178, 2309, 35954, 654797, 13667858, 321839625, 8441614754, 244108628489, 7716226532642, 264711412437133, 9795540525116306, 388938430069794373, 16494335589910579186, 744110964577292267537, 35582626582915655239234
Offset: 1

Views

Author

R. H. Hardin May 28 2012

Keywords

Comments

Diagonal of A212835

Examples

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

Links

A212834 Number of 0..7 arrays of length n+1 with 0 never adjacent to 7.

Original entry on oeis.org

62, 482, 3746, 29114, 226274, 1758602, 13667858, 106226618, 825593474, 6416514026, 49869159026, 387583197338, 3012297335522, 23411580532682, 181954847741906, 1414153417389434, 10990803008177474, 85420541561578922
Offset: 1

Views

Author

R. H. Hardin, May 28 2012

Keywords

Comments

Column 7 of A212835.

Examples

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

Links

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = 7*a(n-1) + 6*a(n-2).
Empirical g.f.: 2*x*(31 + 24*x) / (1 - 7*x - 6*x^2). - Colin Barker, Jul 21 2018

A212836 Number of 0..n arrays of length 3 with 0 never adjacent to n.

Original entry on oeis.org

2, 17, 50, 107, 194, 317, 482, 695, 962, 1289, 1682, 2147, 2690, 3317, 4034, 4847, 5762, 6785, 7922, 9179, 10562, 12077, 13730, 15527, 17474, 19577, 21842, 24275, 26882, 29669, 32642, 35807, 39170, 42737, 46514, 50507, 54722, 59165, 63842, 68759, 73922
Offset: 1

Views

Author

R. H. Hardin, May 28 2012

Keywords

Comments

Row 2 of A212835.

Examples

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

Links

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^3 + 3*n^2 - n - 1.
Conjectures from Colin Barker, Jul 21 2018: (Start)
G.f.: x*(2 + 9*x - 6*x^2 + x^3) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
(End)

A212837 Number of 0..n arrays of length 4 with 0 never adjacent to n.

Original entry on oeis.org

2, 41, 178, 497, 1106, 2137, 3746, 6113, 9442, 13961, 19922, 27601, 37298, 49337, 64066, 81857, 103106, 128233, 157682, 191921, 231442, 276761, 328418, 386977, 453026, 527177, 610066, 702353, 804722, 917881, 1042562, 1179521, 1329538
Offset: 1

Views

Author

R. H. Hardin, May 28 2012

Keywords

Comments

Row 3 of A212835.

Examples

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

Links

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^4 + 4*n^3 - 4*n + 1.
Conjectures from Colin Barker, Jul 21 2018: (Start)
G.f.: x*(2 + 31*x - 7*x^2 - 3*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)

A212838 Number of 0..n arrays of length 5 with 0 never adjacent to n.

Original entry on oeis.org

2, 99, 634, 2309, 6306, 14407, 29114, 53769, 92674, 151211, 235962, 354829, 517154, 733839, 1017466, 1382417, 1844994, 2423539, 3138554, 4012821, 5071522, 6342359, 7855674, 9644569, 11745026, 14196027, 17039674, 20321309, 24089634, 28396831
Offset: 1

Views

Author

R. H. Hardin, May 28 2012

Keywords

Comments

Row 4 of A212835.

Examples

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

Links

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^5 + 5*n^4 + 2*n^3 - 8*n^2 + n + 1.
Conjectures from Colin Barker, Jul 21 2018: (Start)
G.f.: x*(2 + 87*x + 70*x^2 - 50*x^3 + 12*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)

A212839 Number of 0..n arrays of length 6 with 0 never adjacent to n.

Original entry on oeis.org

2, 239, 2258, 10727, 35954, 97127, 226274, 472943, 909602, 1637759, 2794802, 4561559, 7170578, 10915127, 16158914, 23346527, 33014594, 45803663, 62470802, 83902919, 111130802, 145343879, 187905698, 240370127, 304498274, 382276127
Offset: 1

Views

Author

R. H. Hardin, May 28 2012

Keywords

Comments

Row 5 of A212835.

Examples

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

Links

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^6 + 6*n^5 + 5*n^4 - 12*n^3 - 3*n^2 + 6*n - 1.
Conjectures from Colin Barker, Jul 21 2018: (Start)
G.f.: x*(2 + 225*x + 627*x^2 - 130*x^3 - 12*x^4 + 9*x^5 - x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A212840 Number of 0..n arrays of length 7 with 0 never adjacent to n.

Original entry on oeis.org

2, 577, 8042, 49835, 204994, 654797, 1758602, 4159927, 8927810, 17738489, 33102442, 58641827, 99423362, 162351685, 256628234, 394280687, 590768002, 865666097, 1243439210, 1754301979, 2435177282, 3330754877, 4494655882
Offset: 1

Views

Author

R. H. Hardin, May 28 2012

Keywords

Comments

Row 6 of A212835.

Examples

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

Links

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^7 + 7*n^6 + 9*n^5 - 15*n^4 - 13*n^3 + 15*n^2 - 1*n - 1.
Conjectures from Colin Barker, Jul 21 2018: (Start)
G.f.: x*(2 + 561*x + 3482*x^2 + 1543*x^3 - 682*x^4 + 151*x^5 - 18*x^6 + x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

A212841 Number of 0..n arrays of length 8 with 0 never adjacent to n.

Original entry on oeis.org

2, 1393, 28642, 231521, 1168786, 4414417, 13667858, 36590017, 87627106, 192124721, 392074882, 753879073, 1378550642, 2414820241, 4075648306, 6658688897, 10571289538, 16360652017, 24749819426, 36680195041, 53361338962
Offset: 1

Views

Author

R. H. Hardin, May 28 2012

Keywords

Comments

Row 7 of A212835.

Examples

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

Links

Crossrefs

Cf. A212835.

Formula

Empirical: a(n) = n^8 + 8*n^7 + 14*n^6 - 16*n^5 - 30*n^4 + 24*n^3 + 8*n^2 - 8*n + 1.
Conjectures from Colin Barker, Jul 21 2018: (Start)
G.f.: x*(2 + 1375*x + 16177*x^2 + 23723*x^3 - 551*x^4 - 563*x^5 + 179*x^6 - 23*x^7 + x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
Showing 1-8 of 8 results.

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