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 1-6 of 6 results.

A221460 Number of 0..n arrays of length n with each element unequal to at least one neighbor, starting with 0.

Original entry on oeis.org

0, 2, 9, 80, 875, 11880, 192080, 3608576, 77295141, 1860100000, 49701143855, 1460328321024, 46805373800640, 1625353003293824, 60796114850390625, 2437185999638364160, 104248664384022862523, 4739500894223556407808
Offset: 1

Views

Author

R. H. Hardin Jan 17 2013

Keywords

Comments

Diagonal of A221463.

Examples

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

Links

Crossrefs

Cf. A221463.

Formula

a(n) = [x^n] 1/(1 - x*Sum_{k>=1} n^k*x^k). - Ilya Gutkovskiy, Mar 21 2018

A221461 Number of 0..6 arrays of length n with each element unequal to at least one neighbor, starting with 0.

Original entry on oeis.org

0, 6, 36, 252, 1728, 11880, 81648, 561168, 3856896, 26508384, 182191680, 1252200384, 8606352384, 59151316608, 406546013952, 2794183983360, 19204379983872, 131991383803392, 907174582723584, 6234995799161856
Offset: 1

Views

Author

R. H. Hardin Jan 17 2013

Keywords

Comments

Column 6 of A221463

Examples

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

Links

Formula

Empirical: a(n) = 6*a(n-1) +6*a(n-2)

A221462 Number of 0..7 arrays of length n with each element unequal to at least one neighbor, starting with 0.

Original entry on oeis.org

0, 7, 49, 392, 3087, 24353, 192080, 1515031, 11949777, 94253656, 743424031, 5863743809, 46250174880, 364797430823, 2877333239921, 22694914695208, 179005735545903, 1411904551687777, 11136372010635760, 87837935936264759
Offset: 1

Views

Author

R. H. Hardin Jan 17 2013

Keywords

Comments

Column 7 of A221463

Examples

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

Links

Formula

Empirical: a(n) = 7*a(n-1) +7*a(n-2)

A221464 Number of 0..n arrays of length 5 with each element unequal to at least one neighbor, starting with 0.

Original entry on oeis.org

3, 32, 135, 384, 875, 1728, 3087, 5120, 8019, 12000, 17303, 24192, 32955, 43904, 57375, 73728, 93347, 116640, 144039, 176000, 213003, 255552, 304175, 359424, 421875, 492128, 570807, 658560, 756059, 864000, 983103, 1114112, 1257795
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2013

Keywords

Comments

Row 5 of A221463.

Examples

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

Links

Crossrefs

Cf. A221463.

Formula

Empirical: a(n) = 1*n^4 + 2*n^3.
Conjectures from Colin Barker, Aug 05 2018: (Start)
G.f.: x*(3 + 17*x + 5*x^2 - x^3) / (1 - x)^5.
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>5.
(End)

A221465 Number of 0..n arrays of length 6 with each element unequal to at least one neighbor, starting with 0.

Original entry on oeis.org

5, 88, 513, 1856, 5125, 11880, 24353, 45568, 79461, 131000, 206305, 312768, 459173, 655816, 914625, 1249280, 1675333, 2210328, 2873921, 3688000, 4676805, 5867048, 7288033, 8971776, 10953125, 13269880, 15962913, 19076288, 22657381, 26757000
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2013

Keywords

Comments

Row 6 of A221463.

Examples

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

Links

Crossrefs

Cf. A221463.

Formula

Empirical: a(n) = 1*n^5 + 3*n^4 + 1*n^3.
Conjectures from Colin Barker, Aug 05 2018: (Start)
G.f.: x*(5 + 58*x + 60*x^2 - 2*x^3 - x^4) / (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)

A221466 Number of 0..n arrays of length 7 with each element unequal to at least one neighbor, starting with 0.

Original entry on oeis.org

8, 240, 1944, 8960, 30000, 81648, 192080, 405504, 787320, 1430000, 2459688, 4043520, 6397664, 9796080, 14580000, 21168128, 30067560, 41885424, 57341240, 77280000, 102685968, 134697200, 174620784, 223948800, 284375000, 357812208
Offset: 1

Views

Author

R. H. Hardin, Jan 17 2013

Keywords

Comments

Row 7 of A221463.

Examples

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

Links

Crossrefs

Cf. A221463.

Formula

Empirical: a(n) = 1*n^6 + 4*n^5 + 3*n^4.
Conjectures from Colin Barker, Aug 05 2018: (Start)
G.f.: 8*x*(1 + 23*x + 54*x^2 + 14*x^3 - 2*x^4) / (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)
Showing 1-6 of 6 results.

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