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 12 results. Next

A231518 Number of nX3 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

4, 34, 153, 776, 3861, 18721, 91993, 453274, 2223662, 10915727, 53635324, 263420767, 1293604417, 6353594215, 31205396110, 153258629442, 752708346275, 3696838244354, 18156489259107, 89173024237567, 437961215793703
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Column 3 of A231523

Examples

			Some solutions for n=7
..0..1..0....0..0..1....1..0..1....0..0..1....1..0..0....1..0..0....1..0..0
..1..0..0....0..1..1....0..0..0....0..0..1....0..0..0....1..1..0....0..1..1
..1..0..0....0..0..0....1..0..0....0..0..0....1..1..0....1..0..0....1..0..0
..0..0..0....0..0..1....1..0..0....1..0..0....0..0..1....0..0..1....0..0..1
..0..0..0....1..0..0....0..0..0....0..0..1....0..0..0....0..0..0....1..1..0
..0..0..0....0..0..0....0..0..1....0..0..0....0..0..1....1..0..0....1..0..0
..0..0..1....0..1..0....1..0..0....1..1..1....1..1..1....0..0..1....0..0..0
		

Formula

Empirical: a(n) = 4*a(n-1) -2*a(n-2) +43*a(n-3) -50*a(n-4) +33*a(n-5) -307*a(n-6) +115*a(n-7) -66*a(n-8) +490*a(n-9) +60*a(n-10) -144*a(n-11) +32*a(n-12) -192*a(n-13) for n>14

A231519 Number of n X 4 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

7, 107, 865, 7697, 66499, 571226, 4944075, 42759650, 369356733, 3191749214, 27585602947, 238391033438, 2060118342038, 17803462264679, 153856523007378, 1329613892196866, 11490414159104930, 99299276258131228, 858136420916602390
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Column 4 of A231523.

Examples

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

Crossrefs

Cf. A231523.

Formula

Empirical: a(n) = 7*a(n-1) +3*a(n-2) +117*a(n-3) -96*a(n-4) -500*a(n-5) -1683*a(n-6) -40*a(n-7) +4807*a(n-8) +6898*a(n-9) -181*a(n-10) -9621*a(n-11) -10107*a(n-12) -734*a(n-13) -9567*a(n-14) -4385*a(n-15) +24373*a(n-16) +1907*a(n-17) -17636*a(n-18) +2087*a(n-19) +6490*a(n-20) +1542*a(n-21) -233*a(n-22) -560*a(n-23) -36*a(n-24) for n > 25.

A231520 Number of nX5 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

12, 342, 4665, 70462, 1031105, 15000701, 219937967, 3222629836, 47159743290, 690399979855, 10108622083346, 147993608472149, 2166661772771563, 31720960292577983, 464409247083163776, 6799146031063407846
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Column 5 of A231523

Examples

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

Formula

Empirical recurrence of order 70 (see link above)

A231521 Number of nX6 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

21, 1069, 25556, 680302, 17572772, 451200772, 11683058939, 302190345444, 7806399525348, 201765495180944, 5215449996133433, 134798889001969231, 3484039440752712049, 90050899758881308054, 2327507605574582278738
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Column 6 of A231523

Examples

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

A231522 Number of n X 7 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

37, 3381, 144847, 6935963, 322599407, 14940780666, 697702378939, 32529760276112, 1514885617016157, 70592106166184098, 3289771313716069793, 153290011597603312050, 7142830857947956340314, 332840754623625070614641
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Column 7 of A231523.

Examples

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

Crossrefs

Cf. A231523.

A231524 Number of 2 X n 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

4, 10, 34, 107, 342, 1069, 3381, 10689, 33808, 106804, 337525, 1066772, 3371763, 10656541, 33680325, 106448622, 336438736, 1063336915, 3360744286, 10621851017, 33571065345, 106103576857, 335347363656, 1059887498352, 3349844553061
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Examples

			Some solutions for n=7:
  0 1 0 0 0 0 1      1 0 0 0 0 0 1      0 0 0 1 0 0 0
  1 0 0 1 0 1 1      1 0 0 1 0 0 1      0 0 1 0 0 1 0
		

Crossrefs

Row 2 of A231523.

Formula

Empirical: a(n) = 4*a(n-1) - 3*a(n-2) + a(n-3) + 6*a(n-4) - 18*a(n-5).
Empirical g.f.: x*(4 - 6*x + 6*x^2 - 3*x^3 - 18*x^4) / (1 - 4*x + 3*x^2 - x^3 - 6*x^4 + 18*x^5). - Colin Barker, Sep 29 2018

A231525 Number of 3Xn 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

8, 21, 153, 865, 4665, 25556, 144847, 817539, 4574717, 25577718, 143371820, 804082832, 4506873305, 25254564785, 141534685147, 793277267583, 4446076119277, 24918173471356, 139655004825056, 782709245520654
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Row 3 of A231523

Examples

			Some solutions for n=7
..0..0..0..0..1..1..1....0..0..0..0..1..1..0....0..0..0..0..1..1..0
..0..0..1..0..0..0..0....0..0..0..1..0..0..1....0..1..0..0..0..0..0
..1..0..0..0..0..0..0....1..1..0..0..0..0..1....0..0..0..0..1..0..0
		

Formula

Empirical: a(n) = 6*a(n-1) -8*a(n-2) +29*a(n-3) +56*a(n-4) -182*a(n-5) -17*a(n-6) -559*a(n-7) -759*a(n-8) +476*a(n-9) +377*a(n-10) +965*a(n-11) +1048*a(n-12) -43*a(n-13) +15*a(n-14) -384*a(n-15) -335*a(n-16) for n>17

A231526 Number of 4Xn 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

16, 48, 776, 7697, 70462, 680302, 6935963, 69699237, 689683944, 6830674791, 67982605070, 676834294963, 6729716953557, 66892941751789, 665135148008789, 6614505307422976, 65773605302169012, 654010196878214180
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Row 4 of A231523

Examples

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

Formula

Empirical: a(n) = 11*a(n-1) -23*a(n-2) +101*a(n-3) +734*a(n-4) -4730*a(n-5) -1987*a(n-6) -2442*a(n-7) -84415*a(n-8) +350229*a(n-9) +552203*a(n-10) -823403*a(n-11) +1850494*a(n-12) -4878983*a(n-13) -13339933*a(n-14) +14208703*a(n-15) -15634346*a(n-16) +32521122*a(n-17) +144142692*a(n-18) -108237346*a(n-19) +12655781*a(n-20) -18919194*a(n-21) -670476969*a(n-22) +140762199*a(n-23) +132252292*a(n-24) +19031686*a(n-25) +1208538437*a(n-26) +185768242*a(n-27) -177024291*a(n-28) -10977187*a(n-29) -706370171*a(n-30) -253074527*a(n-31) +35399416*a(n-32) +40637687*a(n-33) +185723061*a(n-34) +69289982*a(n-35) -27812168*a(n-36) -32459184*a(n-37) -15021208*a(n-38) -1420800*a(n-39) for n>40

A231527 Number of 5Xn 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

32, 113, 3861, 66499, 1031105, 17572772, 322599407, 5763804982, 100713173563, 1765702022971, 31188391464064, 550845806313494, 9708135650398539, 171046936677051852, 3015450630482773918, 53169280138087861700
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Row 5 of A231523

Examples

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

A231528 Number of 6Xn 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors.

Original entry on oeis.org

64, 261, 18721, 571226, 15000701, 451200772, 14940780666, 476186342599, 14723977144889, 457772945684867, 14379443320523238, 451520043526895518, 14134809455898239484, 442341751627382776887, 13854804160752439932243
Offset: 1

Views

Author

R. H. Hardin, Nov 10 2013

Keywords

Comments

Row 6 of A231523

Examples

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