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 11 results. Next

A267225 Number of length-n 0..n arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

2, 9, 54, 470, 5375, 76237, 1291052, 25415028, 570177387, 14358031083, 400970609974, 12297528376718, 410864493836407, 14852560618944921, 577574220388332600, 24040616483779262824, 1066403330800172463507
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Diagonal of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

A267226 Number of length-n 0..2 arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

3, 9, 21, 47, 103, 223, 479, 1023, 2175, 4607, 9727, 20479, 43007, 90111, 188415, 393215, 819199, 1703935, 3538943, 7340031, 15204351, 31457279, 65011711, 134217727, 276824063, 570425343, 1174405119, 2415919103, 4966055935
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Column 2 of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 5*a(n-1) -8*a(n-2) +4*a(n-3) for n>4.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(3 - 6*x + 2*x^3) / ((1 - x)*(1 - 2*x)^2).
a(n) = 2^(n+1) + 2^(n-2)*n - 1 for n>1.
(End)

A267227 Number of length-n 0..3 arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

4, 16, 54, 176, 564, 1790, 5646, 17732, 55512, 173354, 540258, 1680848, 5221740, 16200758, 50204790, 155413724, 480622848, 1484980802, 4584213642, 14140323560, 43583756436, 134239102286, 413179757214, 1270924525556, 3906925144104
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Column 3 of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 9*a(n-1) - 29*a(n-2) + 39*a(n-3) - 18*a(n-4) for n > 5.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: 2*x*(2 - 10*x + 13*x^2 - x^3 - 3*x^4) / ((1 - x)*(1 - 2*x)*(1 - 3*x)^2).
a(n) = (-9 - 9*2^n + 11*3^(1+n) + 2*3^n*n) / 18 for n>1.
(End)

A267228 Number of length-n 0..4 arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

5, 25, 110, 470, 1980, 8274, 34396, 142474, 588596, 2426738, 9989292, 41065818, 168636772, 691859842, 2836150748, 11617837802, 47559474708, 194575978386, 795613053964, 3251559375226, 13282278193604, 54232112235170
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Column 4 of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 14*a(n-1) -75*a(n-2) +190*a(n-3) -224*a(n-4) +96*a(n-5) for n>6.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(5 - 45*x + 135*x^2 - 145*x^3 + 20*x^4 + 24*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)^2).
a(n) = (2*(-3*2^(1+n) - 8*3^n + 41*4^n - 8) + 3*4^n*n) / 48 for n>1.
(End)

A267229 Number of length-n 0..5 arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

6, 36, 195, 1030, 5375, 27854, 143695, 738990, 3791775, 19421854, 99344735, 507597950, 2591191375, 13217410254, 67376465775, 343259079310, 1747901098175, 8896431461054, 45262405898815, 230195833919070, 1170328696616175, 5948113914182254, 30221815238075855
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Column 5 of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 20*a(n-1) -160*a(n-2) +650*a(n-3) -1399*a(n-4) +1490*a(n-5) -600*a(n-6) for n>7.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(6 - 84*x + 435*x^2 - 1010*x^3 + 969*x^4 - 172*x^5 - 120*x^6) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)^2).
a(n) = (-5*(15 + 5*2^(1+n) + 10*3^n + 15*4^n - 97*5^n) + 12*5^n*n) / 300 for n>1. (End)

A267230 Number of length-n 0..6 arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

7, 49, 315, 1981, 12327, 76237, 469623, 2884909, 17686215, 108259885, 661872471, 4042575277, 24671450343, 150466937773, 917151735159, 5587651325485, 34027698639111, 207144227712301, 1260572274312087, 7668877406965933
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Column 6 of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 27*a(n-1) - 301*a(n-2) + 1785*a(n-3) - 6034*a(n-4) + 11508*a(n-5) - 11304*a(n-6) + 4320*a(n-7) for n > 8.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(7 - 140*x + 1099*x^2 - 4270*x^3 + 8428*x^4 - 7476*x^5 + 1512*x^6 + 720*x^7) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)^2).
a(n) = (-45*2^n - 40*3^n - 45*4^n - 72*5^n + 557*6^n + 5*2^(1 + n)*3^n*n - 72) / 360 for n>1.
(End)

A267231 Number of length-n 0..7 arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

8, 64, 476, 3472, 25088, 180292, 1291052, 9222184, 65755592, 468196540, 3330042548, 23664113536, 168042120176, 1192574364148, 8459259667964, 59977781663128, 425093823838040, 3011867733313516, 21333411555220100
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Column 7 of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = 35*a(n-1) -518*a(n-2) +4214*a(n-3) -20489*a(n-4) +60515*a(n-5) -104992*a(n-6) +96516*a(n-7) -35280*a(n-8) for n>9.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: 4*x*(2 - 54*x + 595*x^2 - 3437*x^3 + 11088*x^4 - 19495*x^5 + 16287*x^6 - 3546*x^7 - 1260*x^8) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)*(1 - 7*x)^2).
a(n) = (-7*(70 + 21*2^(1+n) + 35*3^n + 35*2^(1+n)*3^n + 35*4^n + 42*5^n - 627*7^n) + 60*7^n*n)/2940 for n>1.
(End)

A267233 Number of length-4 0..n arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

6, 47, 176, 470, 1030, 1981, 3472, 5676, 8790, 13035, 18656, 25922, 35126, 46585, 60640, 77656, 98022, 122151, 150480, 183470, 221606, 265397, 315376, 372100, 436150, 508131, 588672, 678426, 778070, 888305, 1009856, 1143472, 1289926
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Comments

Row 4 of A267232.

Examples

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

Links

Crossrefs

Cf. A267232.

Formula

Empirical: a(n) = n^4 + (17/6)*n^3 + 2*n^2 + (1/6)*n.
Conjectures from Colin Barker, Feb 05 2018: (Start)
G.f.: x*(6 + 17*x + x^2) / (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)

A267234 Number of length-5 0..n arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

7, 103, 564, 1980, 5375, 12327, 25088, 46704, 81135, 133375, 209572, 317148, 464919, 663215, 924000, 1260992, 1689783, 2227959, 2895220, 3713500, 4707087, 5902743, 7329824, 9020400, 11009375, 13334607, 16037028, 19160764, 22753255, 26865375
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Examples

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

Links

Crossrefs

Row 5 of A267232.

Formula

Empirical: a(n) = n^5 + (37/12)*n^4 + (5/2)*n^3 + (5/12)*n^2.
Conjectures from Colin Barker, Jan 10 2019: (Start)
G.f.: x*(7 + 61*x + 51*x^2 + x^3) / (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)

A267235 Number of length-6 0..n arrays with no following elements greater than or equal to the first repeated value.

Original entry on oeis.org

8, 223, 1790, 8274, 27854, 76237, 180292, 382404, 745548, 1359083, 2345266, 3866486, 6133218, 9412697, 14038312, 20419720, 29053680, 40535607, 55571846, 74992666, 99765974, 131011749, 170017196, 218252620, 277388020, 349310403
Offset: 1

Views

Author

R. H. Hardin, Jan 12 2016

Keywords

Examples

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

Links

Crossrefs

Row 6 of A267232.

Formula

Empirical: a(n) = n^6 + (197/60)*n^5 + 3*n^4 + (3/4)*n^3 - (1/30)*n.
Conjectures from Colin Barker, Jan 10 2019: (Start)
G.f.: x*(8 + 167*x + 397*x^2 + 147*x^3 + 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)
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