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.

A203356 Number of n X n binary arrays with every 1 immediately preceded by 0 to the left or above.

Original entry on oeis.org

1, 7, 102, 5677, 984703, 572818585, 1089970014327, 6842701992875869, 141313097261182627960, 9609805102278645983838526, 2151172274505675499995093835341, 1585313606427874519807992162372572320
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Diagonal of A203362

Examples

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

Links

A203357 Number of n X 3 binary arrays with every 1 immediately preceded by 0 to the left or above.

Original entry on oeis.org

3, 20, 102, 565, 3042, 16538, 89610, 486103, 2635899, 14295131, 77522409, 420410296, 2279906481, 12364072580, 67051079697, 363621959233, 1971943176024, 10693963589630, 57993991716273, 314504819239756, 1705578083028348
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2011

Keywords

Comments

Column 3 of A203362.

Examples

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

Links

Crossrefs

Cf. A203362.

Formula

Empirical: a(n) = 3*a(n-1) +12*a(n-2) +6*a(n-3) +a(n-4).
Empirical g.f.: x*(3 + 11*x + 6*x^2 + x^3) / (1 - 3*x - 12*x^2 - 6*x^3 - x^4). - Colin Barker, Jun 04 2018

A203358 Number of n X 4 binary arrays with every 1 immediately preceded by 0 to the left or above.

Original entry on oeis.org

5, 61, 565, 5677, 55517, 547897, 5390325, 53087833, 522656405, 5146261573, 50669762053, 498898530085, 4912170264077, 48365462156161, 476208363192837, 4688768398640689, 46165815830098469, 454550623943557645
Offset: 1

Views

Author

R. H. Hardin, Dec 31 2011

Keywords

Comments

Column 4 of A203362.

Examples

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

Links

Crossrefs

Cf. A203362.

Formula

Empirical: a(n) = 5*a(n-1) +42*a(n-2) +54*a(n-3) +23*a(n-4) -7*a(n-5).
Empirical g.f.: x*(5 + 36*x + 50*x^2 + 20*x^3 - 7*x^4) / (1 - 5*x - 42*x^2 - 54*x^3 - 23*x^4 + 7*x^5). - Colin Barker, Jun 04 2018

A203359 Number of nX5 binary arrays with every 1 immediately preceded by 0 to the left or above.

Original entry on oeis.org

8, 182, 3042, 55517, 984703, 17631496, 314688054, 5622720187, 100426911671, 1793946112019, 32044214326230, 572395728321380, 10224472420371970, 182635919619144937, 3262355031315093696, 58274202397081882837
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Column 5 of A203362

Examples

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

Links

Formula

Empirical: a(n) = 8*a(n-1) +148*a(n-2) +471*a(n-3) +578*a(n-4) -25*a(n-5) -302*a(n-6) +171*a(n-7) +90*a(n-8)

A203360 Number of nX6 binary arrays with every 1 immediately preceded by 0 to the left or above.

Original entry on oeis.org

13, 547, 16538, 547897, 17631496, 572818585, 18550312526, 601393482628, 19489674499639, 631692508651393, 20473304776032755, 663554579452002670, 21506172950462296264, 697028243024982135832, 22591098951348605776520
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Column 6 of A203362

Examples

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

Links

Formula

Empirical: a(n) = 13*a(n-1) +510*a(n-2) +3549*a(n-3) +10014*a(n-4) +3375*a(n-5) -26874*a(n-6) -1779*a(n-7) +87219*a(n-8) -58872*a(n-9) -14769*a(n-10) +7653*a(n-11) +130*a(n-12) -433*a(n-13) +39*a(n-14)

A203361 Number of nX7 binary arrays with every 1 immediately preceded by 0 to the left or above.

Original entry on oeis.org

21, 1640, 89610, 5390325, 314688054, 18550312526, 1089970014327, 64114204398028, 3769915844080995, 221699388876599524, 13037021233036033635, 766652822812020772883, 45083423150083817466414, 2651159090798112000786121
Offset: 1

Views

Author

R. H. Hardin Dec 31 2011

Keywords

Comments

Column 7 of A203362

Examples

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

Links

Formula

Empirical: a(n) = 21*a(n-1) +1743*a(n-2) +25515*a(n-3) +156938*a(n-4) +213951*a(n-5) -1636533*a(n-6) -3128592*a(n-7) +23316551*a(n-8) +17066544*a(n-9) -199519590*a(n-10) +291472395*a(n-11) -22194350*a(n-12) -173766021*a(n-13) +129035841*a(n-14) -33578772*a(n-15) -2885164*a(n-16) +4086456*a(n-17) -689631*a(n-18) -24273*a(n-19) +4320*a(n-20) for n>21
Showing 1-6 of 6 results.

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