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 1-9 of 9 results.

A221536 Number of 0..2 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

0, 2, 4, 10, 22, 54, 134, 334, 822, 2014, 4934, 12110, 29750, 73086, 179494, 440750, 1082262, 2657630, 6526342, 16026766, 39356662, 96646974, 237332966, 582812014, 1431196758, 3514554142, 8630600774, 21193942094, 52045411766, 127806567678
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 2 of A221542.

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-1) -2*a(n-2) +4*a(n-4).
Empirical g.f.: 2*x^2*(1 - x + x^2) / (1 - 3*x + 2*x^2 - 4*x^4). - Colin Barker, Oct 18 2017

A221537 Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

0, 3, 8, 30, 103, 364, 1276, 4483, 15740, 55274, 194095, 681576, 2393384, 8404483, 29512736, 103635366, 363920471, 1277923892, 4487489988, 15758032643, 55335074484, 194311722642, 682334774239, 2396050726160, 8413845078800
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 3 of A221542.

Examples

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

Links

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) -a(n-3) +a(n-4).
Empirical g.f.: x^2*(3 - x) / ((1 + x)*(1 - 4*x + 2*x^2 - x^3)). - Colin Barker, Oct 18 2017

A221538 Number of 0..4 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

0, 4, 14, 68, 303, 1386, 6311, 28762, 131012, 596784, 2718469, 12383368, 56409683, 256961576, 1170529586, 5332078812, 24289062227, 110643256974, 504010005519, 2295902089838, 10458455859448, 47641099074536, 217018109737881
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 4 of A221542.

Examples

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

Links

Formula

Empirical: a(n) = 5*a(n-1) -3*a(n-2) +a(n-3) +15*a(n-4) +3*a(n-5) for n>6.
Empirical g.f.: x^2*(4 - 6*x + 10*x^2 + x^3 + x^4) / (1 - 5*x + 3*x^2 - x^3 - 15*x^4 - 3*x^5). - Colin Barker, Oct 18 2017

A221539 Number of 0..5 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

0, 5, 22, 130, 716, 4018, 22466, 125701, 703193, 3933916, 22007609, 123117952, 688762928, 3853170001, 21555920345, 120591020698, 674626461416, 3774085830607, 21113497129178, 118115957356066, 660780130205831
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 5 of A221542.

Examples

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

Links

Formula

Empirical: a(n) = 5*a(n-1) +3*a(n-2) +9*a(n-4) +6*a(n-5) +3*a(n-6).
Empirical g.f.: x^2*(5 - 3*x + 5*x^2 + 3*x^4) / (1 - 5*x - 3*x^2 - 9*x^4 - 6*x^5 - 3*x^6). - Colin Barker, Oct 18 2017

A221540 Number of 0..6 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

0, 6, 32, 222, 1455, 9665, 64047, 424593, 2814515, 18656979, 123673887, 819813575, 5434406883, 36023773275, 238795558499, 1582935756291, 10493015970771, 69556445196155, 461078023878243, 3056408985571563, 20260423189286435
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 6 of A221542.

Examples

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

Links

Formula

Empirical: a(n) = 7*a(n-1) -4*a(n-2) +6*a(n-3) +26*a(n-4) +10*a(n-5) +16*a(n-6) +12*a(n-8).
Empirical g.f.: x^2*(6 - 10*x + 22*x^2 - 7*x^3 + 20*x^4 - 12*x^5 + 6*x^6) / (1 - 7*x + 4*x^2 - 6*x^3 - 26*x^4 - 10*x^5 - 16*x^6 - 12*x^8). - Colin Barker, Oct 18 2017

A221541 Number of 0..7 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

0, 7, 44, 350, 2658, 20386, 156098, 1195561, 9156379, 70126074, 537074685, 4113296146, 31502516844, 241268447450, 1847803587081, 14151780448318, 108384295414048, 830083220654363, 6357361558503534, 48689149448999134
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Column 7 of A221542.

Examples

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

Links

Formula

Empirical: a(n) = 7*a(n-1) +4*a(n-2) +5*a(n-3) +20*a(n-4) +20*a(n-5) +23*a(n-6) -6*a(n-7) +3*a(n-8).
Empirical g.f.: x^2*(7 - 5*x + 14*x^2 - 3*x^3 + 20*x^4 - 6*x^5) / (1 - 7*x - 4*x^2 - 5*x^3 - 20*x^4 - 20*x^5 - 23*x^6 + 6*x^7 - 3*x^8). - Colin Barker, Oct 18 2017

A221543 Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

3, 22, 103, 303, 716, 1455, 2658, 4487, 7128, 10791, 15710, 22143, 30372, 40703, 53466, 69015, 87728, 110007, 136278, 166991, 202620, 243663, 290642, 344103, 404616, 472775, 549198, 634527, 729428, 834591, 950730, 1078583, 1218912
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Row 5 of A221542.

Examples

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

Links

Crossrefs

Cf. A221542.

Formula

Empirical: a(n) = 1*n^4 + 1*n^3 - 3*n^2 + 10*n - 9 for n>3.
Conjectures from Colin Barker, Aug 08 2018: (Start)
G.f.: x*(3 + 7*x + 23*x^2 - 22*x^3 + 26*x^4 - 18*x^5 + 6*x^6 - x^7) / (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>8.
(End)

A221544 Number of 0..n arrays of length 6 with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

5, 54, 364, 1386, 4018, 9665, 20386, 39007, 69242, 115813, 184570, 282611, 418402, 601897, 844658, 1159975, 1562986, 2070797, 2702602, 3479803, 4426130, 5567761, 6933442, 8554607, 10465498, 12703285, 15308186, 18323587, 21796162, 25775993
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Row 6 of A221542.

Examples

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

Links

Crossrefs

Cf. A221542.

Formula

Empirical: a(n) = 1*n^5 + 2*n^4 - 6*n^3 + 21*n^2 - 31*n + 23 for n>4.
Conjectures from Colin Barker, Aug 08 2018: (Start)
G.f.: x*(5 + 24*x + 115*x^2 - 88*x^3 + 157*x^4 - 153*x^5 + 87*x^6 - 34*x^7 + 8*x^8 - x^9) / (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>10.
(End)

A221545 Number of 0..n arrays of length 7 with each element differing from at least one neighbor by something other than 1, starting with 0.

Original entry on oeis.org

8, 134, 1276, 6311, 22466, 64047, 156098, 338711, 672066, 1242191, 2167442, 3605703, 5762306, 8898671, 13341666, 19493687, 27843458, 38977551, 53592626, 72508391, 96681282, 127218863, 165394946, 212665431, 270684866, 341323727
Offset: 1

Views

Author

R. H. Hardin, Jan 19 2013

Keywords

Comments

Row 7 of A221542.

Examples

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

Links

Crossrefs

Cf. A221542.

Formula

Empirical: a(n) = 1*n^6 + 3*n^5 - 8*n^4 + 25*n^3 - 30*n^2 + 20*n - 9 for n>3.
Conjectures from Colin Barker, Aug 08 2018: (Start)
G.f.: x*(8 + 78*x + 506*x^2 - 87*x^3 + 675*x^4 - 822*x^5 + 572*x^6 - 279*x^7 + 79*x^8 - 10*x^9) / (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>10.
(End)
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