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 1-7 of 7 results.

A220328 T(n,k)=Equals two maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..1 nXk array.

Original entry on oeis.org

1, 1, 1, 2, 4, 1, 4, 16, 12, 1, 7, 48, 92, 37, 1, 12, 174, 572, 508, 114, 1, 21, 658, 4062, 6657, 2788, 351, 1, 37, 2482, 29467, 92093, 76627, 15316, 1081, 1, 65, 9229, 213225, 1335202, 2065264, 876714, 84196, 3329, 1, 114, 33982, 1540686, 18836493, 59893608
Offset: 1

Views

Author

R. H. Hardin Dec 10 2012

Keywords

Comments

Table starts
.1.....1.......2.........4..........7.........12.........21........37
.1.....4......16........48........174........658.......2482......9229
.1....12......92.......572.......4062......29467.....213225...1540686
.1....37.....508......6657......92093....1335202...18836493.265346645
.1...114....2788.....76627....2065264...59893608.1653121774
.1...351...15316....876714...46094354.2680626797
.1..1081...84196..10004541.1026529800
.1..3329..462940.114058230
.1.10252.2545492
.1.31572
.1

Examples

			Some solutions for n=3 k=4
..0..0..0..0....0..0..0..0....0..1..0..0....0..0..0..0....0..1..1..1
..0..0..0..0....1..1..0..0....1..0..1..0....1..1..1..1....0..0..1..1
..1..0..1..0....1..1..0..0....1..0..1..0....0..1..1..0....0..0..0..0

Links

Crossrefs

Column 2 is A099098
Row 1 is A005251(n+1)

A220632 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal or antidiagonal neighbors.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 8, 12, 5, 1, 1, 1, 16, 44, 37, 8, 1, 1, 1, 32, 158, 257, 114, 13, 1, 1, 1, 64, 564, 1665, 1481, 351, 21, 1, 1, 1, 128, 2010, 10695, 17527, 8560, 1081, 34, 1, 1, 1, 256, 7160, 68637, 201903, 183961, 49448, 3329, 55, 1, 1, 1, 512
Offset: 1

Views

Author

R. H. Hardin Dec 17 2012

Keywords

Comments

Table starts
.1.1...1......1.........1............1...............1..................1
.1.1...2......4.........8...........16..............32.................64
.1.1...3.....12........44..........158.............564...............2010
.1.1...5.....37.......257.........1665...........10695..............68637
.1.1...8....114......1481........17527..........201903............2329448
.1.1..13....351......8560.......183961.........3817452...........79063898
.1.1..21...1081.....49448......1932695........72097810.........2685329069
.1.1..34...3329....285669.....20301254......1362188752........91163971015
.1.1..55..10252...1650333....213251377.....25734606523......3095401422320
.1.1..89..31572...9534128...2240062837....486186026515....105098157017450
.1.1.144..97229..55079528..23530357757...9185167500820...3568417528948249
.1.1.233.299426.318199485.247170637157.173528846174065.121159087987547537

Examples

			Some solutions for n=3 k=4 0=self 3=ne 4=w 6=e 7=sw (reciprocal directions total 10)
.00.67.46.47...00.67.46.47...00.67.47.00...00.00.00.00...00.00.67.47
.36.46.34.00...36.47.36.47...36.34.00.00...00.00.00.00...00.37.36.47
.00.00.00.00...36.46.34.00...00.00.00.00...00.00.00.00...36.46.34.00

Links

Crossrefs

Column 3 is A000045(n+1)
Column 4 is A099098
Row 2 is A000079(n-2)

A221290 T(n,k) = Equals two maps: number of n X k binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..3 n X k array.

Original entry on oeis.org

1, 1, 1, 2, 4, 1, 4, 16, 12, 1, 7, 52, 92, 37, 1, 12, 200, 673, 556, 114, 1, 21, 792, 5912, 9107, 3332, 351, 1, 37, 3080, 48298, 172904, 123958, 19996, 1081, 1, 65, 12164, 396846, 2890017, 4983598, 1686304, 119972, 3329, 1, 114, 47827, 3240527, 49684593
Offset: 1

Views

Author

R. H. Hardin, Jan 09 2013

Keywords

Comments

Table starts
.1.....1.......2.........4..........7..........12.........21........37
.1.....4......16........52........200.........792.......3080.....12164
.1....12......92.......673.......5912.......48298.....396846...3240527
.1....37.....556......9107.....172904.....2890017...49684593.821323042
.1...114....3332....123958....4983598...172905144.6138441061
.1...351...19996...1686304..143511784.10344276279
.1..1081..119972..22931365.4129628435
.1..3329..719836.311813067
.1.10252.4319012
.1.31572
.1

Examples

			Some solutions for n=3, k=4
..0..0..1..0....0..0..0..0....0..1..0..0....0..0..0..1....0..0..0..1
..0..0..1..0....0..1..0..0....1..0..1..0....0..0..0..0....1..0..0..0
..0..1..0..0....1..0..1..0....1..1..1..0....1..1..0..0....1..1..0..0

Links

Crossrefs

Column 2 is A099098.
Column 3 is A220932.
Column 4 is A220933.
Row 1 is A005251(n+1).
Row 2 is A220936.

A220688 T(n,k)=Number of ways to reciprocally link elements of an nXk array either to themselves or to exactly two horizontal, vertical or antidiagonal neighbors.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 12, 12, 1, 1, 37, 94, 37, 1, 1, 114, 745, 745, 114, 1, 1, 351, 5851, 15452, 5851, 351, 1, 1, 1081, 46027, 312603, 312603, 46027, 1081, 1, 1, 3329, 362057, 6349886, 15978924, 6349886, 362057, 3329, 1, 1, 10252, 2847943, 128995678
Offset: 1

Views

Author

R. H. Hardin Dec 17 2012

Keywords

Comments

Table starts
.1.....1.........1.............1................1....................1
.1.....4........12............37..............114..................351
.1....12........94...........745.............5851................46027
.1....37.......745.........15452...........312603..............6349886
.1...114......5851........312603.........15978924............822649205
.1...351.....46027.......6349886........822649205.........107713940118
.1..1081....362057.....128995678......42362190063.......14108684022136
.1..3329...2847943....2620320833....2181341369109.....1848014307847883
.1.10252..22401961...53226950200..112319870453715...242044667782801540
.1.31572.176214299.1081210102382.5783510938076077.31702119421997470360

Examples

			Some solutions for n=3 k=4 0=self 2=n 3=ne 4=w 6=e 7=sw 8=s (reciprocal directions total 10)
.00.78.00.00...68.46.47.00...00.78.78.00...68.46.46.47...68.46.47.00
.38.26.46.48...28.37.67.48...38.23.27.78...28.67.34.78...28.38.00.78
.26.46.46.24...23.36.46.24...26.34.36.24...23.00.36.24...26.24.36.24

Links

Crossrefs

Column 2 is A099098

A220935 T(n,k)=Equals two maps: number of nXk binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 nXk array.

Original entry on oeis.org

1, 1, 1, 2, 4, 1, 4, 16, 12, 1, 7, 52, 92, 37, 1, 12, 200, 673, 556, 114, 1, 21, 792, 5912, 9107, 3332, 351, 1, 37, 3080, 48212, 172904, 123958, 19996, 1081, 1, 65, 12164, 395844, 2876430, 4983202, 1686304, 119972, 3329, 1, 114, 47827, 3232729, 49406891
Offset: 1

Views

Author

R. H. Hardin Dec 25 2012

Keywords

Comments

Table starts
.1....1......2.......4.......7......12.......21......37....65.114
.1....4.....16......52.....200.....792.....3080...12164.47827
.1...12.....92.....673....5912...48212...395844.3232729
.1...37....556....9107..172904.2876430.49406891
.1..114...3332..123958.4983202
.1..351..19996.1686304
.1.1081.119972
.1.3329
.1

Examples

			Some solutions for n=3 k=4
..0..0..1..1....0..0..1..1....0..0..0..1....0..0..0..1....0..1..0..1
..0..1..1..0....0..1..1..1....1..0..1..1....0..0..0..1....0..0..0..1
..1..1..0..0....0..0..0..0....0..0..0..0....1..0..1..0....1..0..0..0

Crossrefs

Column 2 is A099098
Row 1 is A005251(n+1)

A238236 Expansion of (1-x-x^2)/((x-1)*(x^3+3*x^2+2*x-1)).

Original entry on oeis.org

1, 2, 6, 18, 55, 169, 520, 1601, 4930, 15182, 46754, 143983, 443409, 1365520, 4205249, 12950466, 39882198, 122821042, 378239143, 1164823609, 3587185688, 11047081345, 34020543362, 104769516446, 322647744322, 993624581343, 3059961912097, 9423445312544
Offset: 0

Views

Author

Philippe Deléham, Feb 20 2014

Keywords

Comments

Row sums of the triangle in A152440.

Links

Crossrefs

Cf. A097472, A152440, A099098 (first differences).

Programs

  • Mathematica
    CoefficientList[Series[(1 - x - x^2)/(1 - 3 x - x^2 + 2 x^3 + x^4), {x, 0, 40}], x ](* Vincenzo Librandi, Feb 22 2014 *)

Formula

G.f.: (1-x-x^2)/(1-3*x-x^2+2*x^3+x^4).
a(n) = 3*a(n-1) + a(n-2) -2*a(n-3) - a(n-4), a(0) = 1, a(1) = 2, a(2) = 6, a(3) = 18.
a(n) = A097472(n) - A097472(n-1) - A097472(n-2).
a(n) = A060945(2*n).
a(n)-a(n-1) = A099098(n). - R. J. Mathar, Jun 17 2020

A334293 First quadrisection of Padovan sequence.

Original entry on oeis.org

1, 0, 2, 5, 16, 49, 151, 465, 1432, 4410, 13581, 41824, 128801, 396655, 1221537, 3761840, 11584946, 35676949, 109870576, 338356945, 1042002567, 3208946545, 9882257736, 30433357674, 93722435101, 288627200960, 888855064897, 2737314167775, 8429820731201, 25960439030624
Offset: 0

Views

Author

Oboifeng Dira, Apr 21 2020

Keywords

Examples

			For n=3, a(3) = 2*a(2) + 3*a(1) + a(0) = 2*2 + 3*0 + 1 = 5.

Links

Crossrefs

Quadrisection of A000931.
Bisection (even part) of A099529.
Cf. A099098, A091140.

Programs

  • PARI
    Vec((1 - 2*x - x^2) / (1 - 2*x - 3*x^2 - x^3) + O(x^30)) \\ Colin Barker, Apr 27 2020

Formula

a(n) = A000931(4n).
a(n) = A099529(2n).
a(n) = Sum_{k=0..n} binomial(2*n-k-1, 2*k-1).
a(n) = 2*a(n-1)+3*a(n-2)+a(n-3), a(0)=1, a(1)=0, a(2)=2 for n>=3.
G.f.: (1 - 2*x - x^2) / (1 - 2*x - 3*x^2 - x^3). - Colin Barker, Apr 27 2020
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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