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.

A184200 Number of (n+1) X 3 binary arrays with no 2 X 2 subblock containing fewer than two 1s.

Original entry on oeis.org

35, 195, 1028, 5529, 29593, 158648, 850155, 4556371, 24418812, 130868377, 701364193, 3758831480, 20144755955, 107962068819, 578602594196, 3100912827657, 16618764665065, 89065173542888, 477328206813915
Offset: 1

Views

Author

R. H. Hardin, Jan 10 2011

Keywords

Comments

Column 2 of A184207.

Examples

			Some solutions for 5 X 3:
..0..1..1....1..1..0....1..1..0....1..1..1....0..1..0....0..0..1....1..1..0
..1..0..0....1..0..1....1..0..1....1..1..0....1..1..0....1..1..0....1..1..1
..0..1..1....0..1..1....1..1..0....1..0..1....1..1..1....0..1..1....1..1..0
..1..1..1....0..1..0....1..1..0....0..1..0....0..1..0....1..0..1....0..1..1
..0..1..1....0..1..1....1..0..1....0..1..0....1..1..1....1..0..1....1..0..0
		

Crossrefs

Cf. A184207.

Formula

Empirical: a(n) = 5*a(n-1) + 4*a(n-2) - 11*a(n-3) - a(n-4) + 2*a(n-5).
Empirical g.f.: x*(35 + 20*x - 87*x^2 - 6*x^3 + 16*x^4) / (1 - 5*x - 4*x^2 + 11*x^3 + x^4 - 2*x^5). - Colin Barker, Feb 27 2018

A184201 Number of (n+1)X4 binary arrays with no 2X2 subblock containing fewer than two 1s.

Original entry on oeis.org

108, 1028, 8969, 80812, 721939, 6468501, 57909336, 518574936, 4643443850, 41579555979, 372319892218, 3333908362279, 29853191601007, 267317859115808, 2393674819332654, 21433956109836050, 191928522580951331
Offset: 1

Views

Author

R. H. Hardin Jan 10 2011

Keywords

Comments

Column 3 of A184207

Examples

			Some solutions for 3X4
..1..1..1..1....0..0..1..1....0..1..0..1....1..0..0..1....0..1..0..1
..0..1..1..0....1..1..1..1....1..1..1..1....0..1..1..1....1..1..1..0
..1..1..1..1....1..0..0..1....0..0..0..0....1..1..1..1....0..0..1..1
		

Formula

Empirical: a(n)=9*a(n-1)+8*a(n-2)-79*a(n-3)+19*a(n-4)+134*a(n-5)-54*a(n-6)-56*a(n-7)+23*a(n-8)+5*a(n-9)-2*a(n-10)

A184202 Number of (n+1)X5 binary arrays with no 2X2 subblock containing fewer than two 1s.

Original entry on oeis.org

337, 5529, 80812, 1232795, 18588589, 281420718, 4255603649, 64377477751, 973770904216, 14729764992131, 222807558297931, 3370276970276934, 50980111666109221, 771145138865934865, 11664642166349200910
Offset: 1

Views

Author

R. H. Hardin Jan 10 2011

Keywords

Comments

Column 4 of A184207

Examples

			Some solutions for 3X5
..1..0..1..1..1....0..1..0..1..0....1..1..0..1..1....0..1..1..0..1
..1..1..0..1..1....1..1..1..0..1....1..1..0..1..1....1..1..0..1..0
..0..1..0..1..0....0..1..1..0..1....0..1..1..1..0....1..0..1..1..1
		

Formula

Empirical: a(n)=14*a(n-1)+49*a(n-2)-472*a(n-3)-488*a(n-4)+4808*a(n-5)+278*a(n-6)-15914*a(n-7)+2888*a(n-8)+23043*a(n-9)-5467*a(n-10)-16111*a(n-11)+3566*a(n-12)+5580*a(n-13)-915*a(n-14)-951*a(n-15)+91*a(n-16)+73*a(n-17)-3*a(n-18)-2*a(n-19)

A184203 Number of (n+1) X 6 binary arrays with no 2 X 2 subblock containing fewer than two 1's.

Original entry on oeis.org

1049, 29593, 721939, 18588589, 471487297, 12021784217, 306055720601, 7795714368919, 198537902186962, 5056537169718019, 128782273379145931, 3279904522485716031, 83534449921348607076, 2127503372277866225041
Offset: 1

Views

Author

R. H. Hardin, Jan 10 2011

Keywords

Comments

Column 5 of A184207.

Examples

			Some solutions for 3 X 6
..1..0..1..0..1..1....1..1..0..1..0..1....1..1..0..1..1..0....1..0..1..1..1..1
..1..0..1..1..0..1....1..0..1..1..1..0....1..0..1..0..1..0....1..1..0..0..0..1
..0..1..1..1..1..0....0..1..0..0..1..1....1..1..0..1..0..1....1..0..1..1..1..1
		

Crossrefs

Cf. A184207.

Formula

Empirical: a(n) = 26*a(n-1)+103*a(n-2)-3175*a(n-3)+843*a(n-4)+124668*a(n-5)-241004*a(n-6)-1741528*a(n-7)+4512428*a(n-8)+11666399*a(n-9)-36429185*a(n-10)-41916935*a(n-11)+161955426*a(n-12)+79119202*a(n-13)-435611222*a(n-14)-51541960*a(n-15)+738522868*a(n-16)-83869087*a(n-17)-800207178*a(n-18)+216307031*a(n-19)+552396475*a(n-20)-212199576*a(n-21)-239220431*a(n-22)+114209818*a(n-23)+63085385*a(n-24)-36259721*a(n-25)-9488703*a(n-26)+6873528*a(n-27)+671231*a(n-28)-762566*a(n-29)+22*a(n-30)+47026*a(n-31)-2787*a(n-32)-1453*a(n-33)+139*a(n-34)+17*a(n-35)-2*a(n-36).

A184204 Number of (n+1)X7 binary arrays with no 2X2 subblock containing fewer than two 1s.

Original entry on oeis.org

3268, 158648, 6468501, 281420718, 12021784217, 516844071813, 22178227663588, 952294826074262, 40881902344878662, 1755168245685353119, 75352500961047758574, 3235038360513128954137, 138886585051318322739473
Offset: 1

Views

Author

R. H. Hardin Jan 10 2011

Keywords

Comments

Column 6 of A184207

Examples

			Some solutions for 3X7
..0..1..1..1..1..0..0....0..1..1..1..0..0..1....1..0..1..1..0..0..1
..1..1..1..0..1..1..1....1..1..0..0..1..1..0....1..1..1..0..1..1..0
..0..0..1..0..1..0..0....0..0..1..1..1..1..0....1..1..1..1..1..1..1
		

A184205 Number of (n+1) X 8 binary arrays with no 2 X 2 subblock containing fewer than two 1's.

Original entry on oeis.org

10179, 850155, 57909336, 4255603649, 306055720601, 22178227663588, 1603508113421239, 116023864377980183, 8393076073326616738, 607195930632715485287, 43926429646009509917693, 3177799102996723675846736
Offset: 1

Views

Author

R. H. Hardin, Jan 10 2011

Keywords

Comments

Column 7 of A184207.

Examples

			Some solutions for 3 X 8
..0..0..1..1..0..1..1..0....0..0..0..0..0..1..1..1....0..0..1..1..1..1..0..0
..1..1..0..1..1..1..0..1....1..1..1..1..1..0..1..1....1..1..1..1..0..1..1..1
..1..1..1..1..1..1..1..1....0..0..1..1..0..1..1..0....1..1..0..1..0..1..0..1
		

Crossrefs

Cf. A184207.

A184206 Number of (n+1)X9 binary arrays with no 2X2 subblock containing fewer than two 1s.

Original entry on oeis.org

31707, 4556371, 518574936, 64377477751, 7795714368919, 952294826074262, 116023864377980183, 14148460147460008963, 1724850427268614620086, 210297145807804211632731, 25639101187522824504622401
Offset: 1

Views

Author

R. H. Hardin Jan 10 2011

Keywords

Comments

Column 8 of A184207

Examples

			Some solutions for 3X9
..0..0..0..0..1..0..0..1..1....0..0..0..1..0..0..1..0..1
..1..1..1..1..1..1..1..0..0....1..1..1..0..1..1..1..1..0
..1..0..0..0..0..1..1..1..1....0..0..1..1..0..1..1..0..1
		
Showing 1-7 of 7 results.