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.

A205305 Number of nX3 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

Original entry on oeis.org

4, 159, 7445, 381958, 19490790, 996536552, 50933680120, 2603456557653, 133072628448179, 6801873967993408, 347670725973943044, 17770830778194675356, 908337669425005770376, 46428742540607711341143
Offset: 1

Views

Author

R. H. Hardin Jan 25 2012

Keywords

Comments

Column 3 of A205310

Examples

			Some solutions for n=5
..0..0..1....0..0..1....0..0..1....0..0..1....0..1..0....0..1..1....0..0..1
..0..2..0....0..1..0....1..2..1....2..0..2....1..0..0....2..1..1....2..0..3
..3..1..1....2..2..1....1..3..2....2..1..1....0..1..1....0..2..0....3..1..1
..2..0..2....1..3..2....0..3..3....0..1..1....1..0..2....3..0..0....0..1..2
..0..1..0....0..1..0....0..1..3....2..2..3....3..0..1....2..1..1....1..2..0
		

Formula

Empirical: a(n) = 45*a(n-1) +360*a(n-2) -2443*a(n-3) +752*a(n-4) +1861*a(n-5) +17330*a(n-6) +3931*a(n-7) -55696*a(n-8) -6621*a(n-9) +28764*a(n-10) -5265*a(n-11) -9477*a(n-12) +1080*a(n-13) +1080*a(n-14)

A205306 Number of nX4 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

Original entry on oeis.org

12, 2191, 381958, 70985206, 13049279920, 2404472055439, 442834241887042, 81565593153176155, 15023237028425135528, 2767081708267517685850, 509659402434339115696776, 93872456554136530629815555
Offset: 1

Views

Author

R. H. Hardin Jan 25 2012

Keywords

Comments

Column 4 of A205310

Examples

			Some solutions for n=5
..0..1..0..2....0..0..1..0....0..0..1..2....0..0..1..0....0..0..1..1
..0..3..3..0....0..2..1..3....0..2..2..1....0..0..1..2....1..0..2..1
..1..3..2..1....2..0..2..0....1..0..1..1....1..1..2..3....0..1..0..2
..1..2..1..1....2..0..1..2....2..2..1..0....1..3..3..1....2..1..0..3
..0..2..0..3....1..3..0..0....0..3..0..0....2..3..0..1....1..0..1..0
		

Formula

Empirical: a(n) = 138*a(n-1) +9087*a(n-2) -80152*a(n-3) -5124946*a(n-4) +37705868*a(n-5) +99346827*a(n-6) +17722141556*a(n-7) -261185384994*a(n-8) +714699066626*a(n-9) -15202912141613*a(n-10) +304934550079298*a(n-11) -1225389716322737*a(n-12) -933781202067468*a(n-13) -33805706864300454*a(n-14) +185474258286271178*a(n-15) +1505623972530492162*a(n-16) -5117407741799018012*a(n-17) -25380195891304445642*a(n-18) +36229117914918274800*a(n-19) +251716664318924304110*a(n-20) -57605851368069887202*a(n-21) -1572473827570790923150*a(n-22) +3125955801166175823856*a(n-23) +17062517535287193726997*a(n-24) -32422586388875348507390*a(n-25) -159910400746542325205407*a(n-26) +54332608228198865319136*a(n-27) +661022488412915752154803*a(n-28) -721321139998771867284976*a(n-29) -3898866024012351846512850*a(n-30) +8412783886991366949353912*a(n-31) +30366027249263904221568708*a(n-32) -31118625776087432549655374*a(n-33) -111729795190877573537105846*a(n-34) +173816789359823529339671964*a(n-35) +553846546751160710968339655*a(n-36) -491036374242582108130054650*a(n-37) -2388488759973180614259754299*a(n-38) +22872473135117365385257812*a(n-39) +3637708187356950277191989337*a(n-40) -5888644440469728116298052320*a(n-41) -11635513023181409403942859614*a(n-42) +21091653515446386649943887296*a(n-43) +46583550442447069247305690806*a(n-44) -12430137563792000600050770102*a(n-45) -75388261189276904319964385046*a(n-46) +5063083350236789682463303536*a(n-47) +82424407966823722700175286140*a(n-48) -21774887291888889019777511748*a(n-49) -57879941791365958357832645088*a(n-50) +37727395614936350378426942136*a(n-51) +19448471990119789641851858295*a(n-52) -25295452552287517410871856028*a(n-53) -1750790964891024780004737837*a(n-54) +8054517038069608971655873284*a(n-55) +238128699519517099475692602*a(n-56) -2376060075223639793908923996*a(n-57) -401856855452402783889059865*a(n-58) +1146937237342456226969479554*a(n-59) +181659002124956734165606650*a(n-60) -391677684362411951192598594*a(n-61) -58125167210869815728999295*a(n-62) +77982926942952062273163618*a(n-63) -1014467950258371834786963*a(n-64) -13318075675102589346103236*a(n-65) -2967557913938184769133316*a(n-66) +12477808904841273824317728*a(n-67) +4694214069617141148458976*a(n-68) -6736162769502273391513536*a(n-69) -1685763587529755229146112*a(n-70) +1487182043605291803500544*a(n-71) +445045584055138381209600*a(n-72) -248152311461700801478656*a(n-73) -19790145808333878067200*a(n-74) +11874087485000326840320*a(n-75)

A205307 Number of n X 5 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

Original entry on oeis.org

40, 31168, 19490790, 13049279920, 8615950028840, 5705396521337690, 3775750320744043966, 2499057571450100571862, 1654008038632602002195374, 1094715856585124185784208270, 724543877252168299768908602288, 479543578578238224536612339956838, 317388689777679827724542588307647638
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2012

Keywords

Examples

			Some solutions for n=5:
..0..0..1..1..2....0..1..0..1..0....0..1..1..0..0....0..1..0..2..0
..0..2..2..1..2....0..0..1..1..2....0..0..1..0..0....3..3..0..1..3
..1..0..1..0..3....3..2..3..0..1....1..2..3..1..1....2..1..1..2..1
..2..0..1..3..2....1..1..2..2..1....2..0..1..0..0....1..0..2..0..3
..0..1..0..0..1....2..3..0..1..2....0..0..3..0..1....0..0..2..1..1
		

Crossrefs

Column 5 of A205310.

A205304 Number of n X n 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 15, 7445, 70985206, 8615950028840, 13585407518869992739
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2012

Keywords

Examples

			Some solutions for n=5
..0..1..0..0..1....0..0..1..0..0....0..0..1..0..0....0..0..1..1..0
..0..0..1..2..1....2..1..3..2..2....2..0..3..0..2....0..1..0..0..2
..3..1..3..0..0....2..2..3..2..2....0..3..1..1..2....1..1..0..0..3
..1..0..2..0..1....3..1..1..3..1....0..2..0..1..0....1..3..1..1..0
..0..2..0..1..1....1..2..1..3..2....3..2..2..3..2....2..3..2..3..1
		

Crossrefs

Diagonal of A205310.

A205308 Number of n X 6 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

Original entry on oeis.org

143, 447343, 996536552, 2404472055439, 5705396521337690, 13585407518869992739, 32325164995795813807941, 76926439840751174108312233, 183061289081893168962560628406
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2012

Keywords

Examples

			Some solutions for n=5
..0..0..1..2..3..3....0..0..1..0..0..1....0..0..1..0..0..2....0..0..1..2..0..2
..2..3..0..0..1..2....1..2..1..0..1..3....1..3..2..2..3..2....2..1..1..0..1..1
..3..2..2..0..2..1....1..3..3..1..1..3....3..2..2..3..1..1....2..2..3..0..0..3
..0..1..2..1..3..2....0..1..0..0..2..0....2..1..1..2..1..3....0..0..1..1..2..3
..1..3..0..3..1..0....0..1..1..3..3..0....2..3..1..0..0..1....3..3..2..0..0..2
		

Crossrefs

Column 6 of A205310.

A205309 Number of n X 7 0..3 arrays with no occurrence of three equal elements in a row horizontally or vertically, and new values 0..3 introduced in row major order.

Original entry on oeis.org

528, 6427791, 50933680120, 442834241887042, 3775750320744043966, 32325164995795813807941
Offset: 1

Views

Author

R. H. Hardin, Jan 25 2012

Keywords

Examples

			Some solutions for n=5
..0..0..1..0..0..1..1....0..1..2..2..1..0..0....0..1..1..0..0..2..3
..2..1..0..1..3..1..3....3..0..0..1..1..2..3....3..0..0..2..1..3..2
..3..1..1..3..0..2..0....3..3..2..0..0..2..1....0..1..0..2..0..1..2
..0..2..0..0..1..1..3....1..3..1..0..0..1..0....1..3..1..0..1..3..3
..3..0..3..1..1..3..2....2..0..2..1..1..0..3....2..0..2..2..1..1..0
		

Crossrefs

Column 7 of A205310.
Showing 1-6 of 6 results.