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 1-6 of 6 results.

A203372 Number of (n+1)X(n+1) 0..1 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

12, 164, 5208, 387324, 67731264, 27913330472, 27149753088792, 62383316832685348, 338853014329060508760, 4353185098169744392741448, 132316928041105714306034574480, 9518293354852895518368238072987352
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Diagonal of A203378

Examples

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

A203373 Number of (n+1) X 4 0..1 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

108, 748, 5208, 36300, 253068, 1764360, 12301020, 85762188, 597930552, 4168748268, 29064349260, 202635502632, 1412766774396, 9849754525644, 68672102130648, 478779201937548, 3338029812632076, 23272612897409352
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2011

Keywords

Comments

Column 3 of A203378.

Examples

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

Crossrefs

Cf. A203378.

Formula

Empirical: a(n) = 9*a(n-1) -15*a(n-2) +6*a(n-3).
Empirical g.f.: 4*x*(27 - 56*x + 24*x^2) / (1 - 9*x + 15*x^2 - 6*x^3). - Colin Barker, Jun 04 2018

A203374 Number of (n+1) X 5 0..1 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

324, 3412, 36300, 387324, 4136292, 44183028, 471988172, 5042151644, 53864590276, 575428804372, 6147238485228, 65670238411324, 701547599923492, 7494552376793140, 80063441950649100, 855308552375931036
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2011

Keywords

Comments

Column 4 of A203378.

Examples

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

Crossrefs

Cf. A203378.

Formula

Empirical: a(n) = 16*a(n-1) -65*a(n-2) +92*a(n-3) -48*a(n-4) +8*a(n-5).
Empirical g.f.: 4*x*(81 - 443*x + 692*x^2 - 376*x^3 + 64*x^4) / (1 - 16*x + 65*x^2 - 92*x^3 + 48*x^4 - 8*x^5). - Colin Barker, Jun 04 2018

A203375 Number of (n+1)X6 0..1 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

972, 15564, 253068, 4136292, 67731264, 1109832180, 18189909480, 298154846436, 4887277903812, 80111933563464, 1313194979326320, 21525927546323460, 352853780193705264, 5783993041849734792, 94811448308361126864
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Column 5 of A203378

Examples

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

Formula

Empirical: a(n) = 30*a(n-1) -291*a(n-2) +1278*a(n-3) -2901*a(n-4) +3519*a(n-5) -2152*a(n-6) +516*a(n-7)

A203376 Number of (n+1)X7 0..1 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

2916, 70996, 1764360, 44183028, 1109832180, 27913330472, 702420750924, 17679917387404, 445045123432096, 11203277447970636, 282028756620227124, 7099777698513424920, 178729975670304808348, 4499358353656818662428
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Column 6 of A203378

Examples

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

Formula

Empirical: a(n) = 55*a(n-1) -1109*a(n-2) +11330*a(n-3) -67206*a(n-4) +247404*a(n-5) -582440*a(n-6) +881876*a(n-7) -846764*a(n-8) +499200*a(n-9) -172400*a(n-10) +33152*a(n-11) -3264*a(n-12) +128*a(n-13)

A203377 Number of (n+1)X8 0..1 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements.

Original entry on oeis.org

8748, 323852, 12301020, 471988172, 18189909480, 702420750924, 27149753088792, 1049837466171436, 40603753889665632, 1570549319417597656, 60751409051086135560, 2350012855527394133452, 90905131505907584858388
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Column 7 of A203378

Examples

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

Formula

Empirical: a(n) = 105*a(n-1) -4473*a(n-2) +105654*a(n-3) -1580037*a(n-4) +16082595*a(n-5) -116408090*a(n-6) +616031475*a(n-7) -2425718097*a(n-8) +7181467374*a(n-9) -16063429749*a(n-10) +27150592284*a(n-11) -34525830041*a(n-12) +32730104655*a(n-13) -22785383754*a(n-14) +11380763892*a(n-15) -3932260752*a(n-16) +884206944*a(n-17) -115250048*a(n-18) +6527616*a(n-19)
Showing 1-6 of 6 results.