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

A231413 Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

9, 50, 285, 1617, 9188, 52193, 296511, 1684466, 9569425, 54363701, 308839124, 1754508933, 9967330587, 56624207962, 321681006005, 1827463435305, 10381783646596, 58978707645369, 335056872107879, 1903451466275938
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Column 1 of A231419.

Examples

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

Crossrefs

Cf. A231419.

Formula

Empirical: a(n) = 6*a(n-1) - 11*a(n-3) + 4*a(n-4).
Empirical g.f.: x*(9 - 4*x - 15*x^2 + 6*x^3) / (1 - 6*x + 11*x^3 - 4*x^4). - Colin Barker, Feb 21 2018

A231414 Number of (n+1)X(2+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

71, 1032, 15125, 221445, 3245016, 47557773, 697029563, 10216062982, 149732672641, 2194570662617, 32164925750976, 471428170136401, 6909529986297263, 101270156563366358, 1484275287919713541
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Column 2 of A231419

Examples

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

Formula

Empirical: a(n) = 17*a(n-1) -28*a(n-2) -119*a(n-3) +373*a(n-4) +134*a(n-5) -268*a(n-6) -200*a(n-7)

A231415 Number of (n+1)X(3+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

514, 20896, 844061, 34099824, 1378646988, 55743171795, 2253925687328, 91135639532050, 3684995866308397, 148999828418108116, 6024687611678499118, 243603373370750396584, 9849905481191885220441, 398272965802692213756388
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Column 3 of A231419

Examples

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

Formula

Empirical: a(n) = 46*a(n-1) -196*a(n-2) -1267*a(n-3) +3292*a(n-4) +14529*a(n-5) +171276*a(n-6) -1140184*a(n-7) -4475862*a(n-8) +10969543*a(n-9) +62966783*a(n-10) +91108201*a(n-11) +282085660*a(n-12) +647957840*a(n-13) -2319416710*a(n-14) -7818927246*a(n-15) -4993117801*a(n-16) +1684239825*a(n-17) +21907839370*a(n-18) +51944554645*a(n-19) +32558644866*a(n-20) -56438925441*a(n-21) -129903082195*a(n-22) -6021907645*a(n-23) -46647268966*a(n-24) +81404415386*a(n-25) +152792965116*a(n-26) -57732537680*a(n-27) +39345285424*a(n-28) -41777158208*a(n-29) -29468075264*a(n-30) +16816004096*a(n-31) +1488514048*a(n-32) -205930496*a(n-33) -244383744*a(n-34)

A231416 Number of (n+1)X(4+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

3838, 424404, 46978621, 5203044823, 576572713438, 63894846010493, 7080853332198865, 784704141897864326, 86961390140923819589, 9637114526684569688989, 1067990945993822381880678
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Column 4 of A231419

Examples

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

Formula

Empirical recurrence of order 99 (see link above)

A231417 Number of (n+1)X(5+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

28486, 8704406, 2655479347, 811353885448, 248018799189236, 75819176620140996, 23178359868994047219, 7085768089483888477664, 2166164383665763734001402, 662210265083703521871876846, 202441903792716290658255634928
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Column 5 of A231419

Examples

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

A231420 Number of (1+1) X (n+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

9, 71, 514, 3838, 28486, 212060, 1578180, 11748804, 87465304, 651171800, 4847955288, 36093104816, 268714229264, 2000587354768, 14894452176096, 110889806477664, 825579209354848, 6146471657514944, 45760738536130624
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Examples

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

Crossrefs

Row 1 of A231419.

Formula

Empirical: a(n) = 8*a(n-1) + 4*a(n-2) - 58*a(n-3) - 24*a(n-4) + 40*a(n-5) - 16*a(n-6).
Empirical g.f.: x*(9 - x - 90*x^2 - 36*x^3 + 60*x^4 - 24*x^5) / (1 - 8*x - 4*x^2 + 58*x^3 + 24*x^4 - 40*x^5 + 16*x^6). - Colin Barker, Sep 28 2018

A231421 Number of (2+1)X(n+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

50, 1032, 20896, 424404, 8704406, 178277756, 3654045516, 74894704740, 1535161355750, 31467342399888, 645012980337444, 13221399981059518, 271010854744794084, 5555152819316036170, 113868962991822419034
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Row 2 of A231419

Examples

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

Formula

Empirical: a(n) = 20*a(n-1) +56*a(n-2) -821*a(n-3) -2559*a(n-4) +2274*a(n-5) +11333*a(n-6) +75045*a(n-7) +58970*a(n-8) -744820*a(n-9) -338743*a(n-10) +3350990*a(n-11) -566226*a(n-12) -8533262*a(n-13) +6626396*a(n-14) +10836980*a(n-15) -13238580*a(n-16) -6337152*a(n-17) +13746128*a(n-18) -1255112*a(n-19) -8079152*a(n-20) +2081168*a(n-21) +460736*a(n-22) -1034208*a(n-23) +221216*a(n-24) -114304*a(n-25) -122880*a(n-26) -16384*a(n-27) -512*a(n-28)

A231422 Number of (3+1)X(n+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

285, 15125, 844061, 46978621, 2655479347, 149618567148, 8438399440722, 475900619492206, 26841006150186265, 1513850582045527801, 85382577970170683674, 4815661653900157997070, 271608188052392844879540
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Row 3 of A231419

Examples

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

A231423 Number of (4+1)X(n+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

1617, 221445, 34099824, 5203044823, 811353885448, 125876025896444, 19554586025933205, 3037479673157123589, 471854862731482999906, 73300037772908376296760, 11386807913185698630539497
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Row 4 of A231419

Examples

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

A231424 Number of (5+1)X(n+1) 0..2 arrays with no element equal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.

Original entry on oeis.org

9188, 3245016, 1378646988, 576572713438, 248018799189236, 105946496489105569, 45332709618289157734, 19394314328543249729459, 8297981425441388783508671, 3550343374214975133494877631, 1519044304273096909835045727359
Offset: 1

Views

Author

R. H. Hardin, Nov 08 2013

Keywords

Comments

Row 5 of A231419

Examples

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