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 1-8 of 8 results.

A188501 Number of n X 2 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

4, 16, 49, 144, 441, 1369, 4225, 12996, 40000, 123201, 379456, 1168561, 3598609, 11082241, 34128964, 105103504, 323676081, 996791184, 3069714025, 9453478441, 29112890625, 89655929476, 276104007936, 850288696321, 2618545348864
Offset: 1

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Author

R. H. Hardin, Apr 02 2011

Keywords

Comments

Column 2 of A188508.

Examples

			Some solutions for 3 X 2:
..1..1....0..1....1..1....1..1....0..1....1..0....0..1....1..1....1..1....0..1
..1..0....1..0....1..1....0..0....0..1....1..0....0..0....0..1....0..1....0..0
..1..0....1..0....1..0....1..0....1..1....0..1....1..1....1..1....1..0....1..0
		

Formula

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

A188502 Number of nX3 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

7, 49, 229, 971, 4351, 20124, 92597, 423074, 1932355, 8836938, 40424590, 184890099, 845559045, 3867059514, 17685848557, 80885615913, 369926354240, 1691838530486, 7737537171921, 35387239493020, 161841764228828, 740175150497968
Offset: 1

Views

Author

R. H. Hardin Apr 02 2011

Keywords

Comments

Column 3 of A188508

Examples

			Some solutions for 4X3
..1..1..1....1..0..1....1..0..1....1..1..0....1..1..1....1..0..0....1..1..1
..1..0..0....1..0..1....0..0..1....0..0..0....1..1..1....0..0..0....0..0..1
..1..0..0....1..0..1....0..1..1....0..0..0....0..0..0....1..0..0....0..0..1
..1..0..1....1..1..1....0..1..1....1..0..0....0..0..0....1..0..0....1..1..0
		

Formula

Empirical: a(n)=7*a(n-1)-21*a(n-2)+59*a(n-3)-82*a(n-4)+97*a(n-5)-14*a(n-6)-148*a(n-7)+166*a(n-8)-153*a(n-9)-158*a(n-10)+340*a(n-11)+164*a(n-12)-296*a(n-13)-87*a(n-14)+115*a(n-15)+13*a(n-16)-a(n-17)+6*a(n-18)-5*a(n-19)-6*a(n-20)+4*a(n-21)+a(n-23)

A188503 Number of nX4 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

12, 144, 971, 5626, 35079, 230877, 1512392, 9787958, 63259244, 409715970, 2655276933, 17202889943, 111435906926, 721881185963, 4676493715792, 30295147280715, 196256042632128, 1271373728805624, 8236145058768675
Offset: 1

Views

Author

R. H. Hardin Apr 02 2011

Keywords

Comments

Column 4 of A188508

Examples

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

Formula

Empirical: a(n)=12*a(n-1)-66*a(n-2)+288*a(n-3)-815*a(n-4)+1743*a(n-5)-2170*a(n-6)-708*a(n-7)+8571*a(n-8)-24260*a(n-9)+29061*a(n-10)+8757*a(n-11)-82862*a(n-12)+174658*a(n-13)+5251*a(n-14)-402534*a(n-15)-22429*a(n-16)+556322*a(n-17)+375232*a(n-18)-748378*a(n-19)-418312*a(n-20)+424506*a(n-21)+47333*a(n-22)+402792*a(n-23)-186063*a(n-24)-330688*a(n-25)+259289*a(n-26)-135270*a(n-27)+300693*a(n-28)+100812*a(n-29)+43040*a(n-30)-78752*a(n-31)-308217*a(n-32)+52646*a(n-33)-163853*a(n-34)+477*a(n-35)-19108*a(n-36)-71235*a(n-37)+9813*a(n-38)+1325*a(n-39)-4720*a(n-40)+32306*a(n-41)+5043*a(n-42)+6561*a(n-43)+1460*a(n-44)-658*a(n-45)-831*a(n-46)-617*a(n-47)-163*a(n-48)-40*a(n-49)-2*a(n-50)+8*a(n-51)+a(n-53)

A188504 Number of nX5 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

21, 441, 4351, 35079, 317751, 3121877, 30288308, 288040928, 2737303569, 26117921403, 249374820339, 2379330844064, 22697020589721, 216539527325714, 2065979971938958, 19710827779239843, 188052454261718490
Offset: 1

Views

Author

R. H. Hardin Apr 02 2011

Keywords

Comments

Column 5 of A188508

Examples

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

A188505 Number of nX6 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

37, 1369, 20124, 230877, 3121877, 47153387, 697038111, 10000092025, 143394872372, 2069826687060, 29910249762049, 431680548664164, 6227868813269851, 89869161823226891, 1296951083139645799
Offset: 1

Views

Author

R. H. Hardin Apr 02 2011

Keywords

Comments

Column 6 of A188508

Examples

			Some solutions for 3X6
..1..1..1..1..1..1....1..1..1..0..0..1....1..1..1..1..0..1....1..1..1..1..0..1
..1..1..1..0..0..1....1..1..0..0..0..1....1..1..1..0..0..1....0..0..0..1..1..0
..1..0..0..1..1..1....1..1..0..1..1..1....1..0..0..1..1..1....1..1..1..1..1..0
		

A188506 Number of nX7 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

65, 4225, 92597, 1512392, 30288308, 697038111, 15602080066, 335304991524, 7194757384224, 155853551899068, 3383311479703509, 73314613539836869, 1587497536509020156, 34383826361857099073, 744867940878570173157
Offset: 1

Views

Author

R. H. Hardin Apr 02 2011

Keywords

Comments

Column 7 of A188508

Examples

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

A188507 Number of nX8 binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

114, 12996, 423074, 9787958, 288040928, 10000092025, 335304991524, 10679333746605, 339310586309097, 10918718979436711, 352511901498687057, 11353212589309062333, 365199323625699877767, 11751342219622127826211
Offset: 1

Views

Author

R. H. Hardin Apr 02 2011

Keywords

Comments

Column 8 of A188508

Examples

			Some solutions for 3X8
..0..1..1..0..0..0..0..0....0..0..1..1..1..1..0..0....0..1..1..1..0..0..0..1
..0..1..1..0..0..0..0..0....0..0..0..0..0..1..1..0....0..1..1..0..0..1..1..0
..1..0..1..1..1..1..1..0....1..1..1..0..1..1..1..1....0..0..1..1..1..1..1..1
		

A188500 Number of n X n binary arrays without the pattern 0 1 0 diagonally, vertically or horizontally.

Original entry on oeis.org

2, 16, 229, 5626, 317751, 47153387, 15602080066, 10679333746605, 15965188461370862, 54469837118110826481, 418222453639358665952917, 7076429422309098758072976354, 264209106726567934754362229986426
Offset: 1

Views

Author

R. H. Hardin Apr 02 2011

Keywords

Comments

Diagonal of A188508

Examples

			Some solutions for 3X3
..1..1..1....1..1..1....1..0..1....0..0..0....0..0..1....0..0..1....1..0..0
..1..1..1....0..0..0....1..0..0....1..0..0....0..0..0....0..0..1....1..0..1
..0..0..1....1..1..1....0..0..0....1..1..1....0..0..0....1..1..0....1..1..1
		
Showing 1-8 of 8 results.