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.

A209497 Number of n X 2 0..4 arrays with every 2 X 2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order.

Original entry on oeis.org

2, 6, 57, 690, 9393, 133380, 1920126, 27760512, 401882796, 5820335088, 84304518360, 1221153876288, 17688664980912, 256224877720896, 3711487617186912, 53761934301895680, 778756709322725568
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Column 2 of A209503.

Examples

			Some solutions for n=4.
..0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..0....0..1....0..0
..1..2....1..2....0..2....1..2....1..2....1..2....1..2....1..2....1..2....1..2
..3..1....2..0....1..0....0..1....2..3....0..2....1..0....0..1....0..2....2..3
..2..1....0..3....2..0....0..2....2..1....3..2....2..0....2..1....1..0....4..2
		

Crossrefs

Cf. A209503.

Formula

Empirical: a(n) = 16*a(n-1) - 10*a(n-2) - 168*a(n-3) - 72*a(n-4) for n>5.
Empirical g.f.: x*(2 - 26*x - 19*x^2 + 174*x^3 + 75*x^4) / ((1 - 4*x - 2*x^2)*(1 - 12*x - 36*x^2)). - Colin Barker, Jul 10 2018

A209498 Number of nX3 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order.

Original entry on oeis.org

5, 57, 1938, 78135, 3268686, 137627625, 5801378991, 244591579065, 10312560758853, 434804544586449, 18332515897436133, 772947757887140085, 32589539696259731973, 1374061949636494558605, 57934118148061257233025
Offset: 1

Views

Author

R. H. Hardin Mar 09 2012

Keywords

Comments

Column 3 of A209503

Examples

			Some.solutions.for.n=4
..0..0..1....0..1..2....0..0..0....0..1..0....0..1..0....0..1..2....0..1..1
..2..3..3....2..1..3....1..2..3....2..1..2....2..2..2....0..3..3....0..2..0
..4..2..1....1..4..1....0..1..2....3..1..0....3..0..1....0..4..0....1..1..2
..2..0..1....3..1..2....1..3..3....3..2..1....2..2..0....2..4..1....2..0..2
		

Formula

Empirical: a(n) = 52*a(n-1) -388*a(n-2) -1564*a(n-3) +19075*a(n-4) -29776*a(n-5) -22290*a(n-6) +50544*a(n-7) -5832*a(n-8) for n>9

A209499 Number of nX4 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order.

Original entry on oeis.org

15, 690, 78135, 9502354, 1165032679, 142937856372, 17538444837670, 2151975129988088, 264048573957784964, 32398910709148727392, 3975364904849935772656, 487779550353892225564624
Offset: 1

Views

Author

R. H. Hardin Mar 09 2012

Keywords

Comments

Column 4 of A209503

Examples

			Some.solutions.for.n=4
..0..1..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..1..2..1..2....1..2..3..2....1..2..3..4....1..2..1..3....1..2..3..1
..0..0..0..2....0..0..3..4....1..3..4..0....3..2..0..1....4..4..4..1
..1..2..1..2....4..3..4..0....2..2..4..3....0..0..3..3....0..2..1..0
		

Formula

Empirical: a(n) = 118*a(n-1) +1604*a(n-2) -127784*a(n-3) -79452*a(n-4) +37606360*a(n-5) -178547756*a(n-6) -2931053296*a(n-7) +18312307424*a(n-8) +74021561744*a(n-9) -495233537616*a(n-10) -1023076292096*a(n-11) +5490220477440*a(n-12) +8804921243328*a(n-13) -24309394624512*a(n-14) -36012394278144*a(n-15) +28360887229440*a(n-16) +27667991881728*a(n-17) -15907925311488*a(n-18) for n>19

A209500 Number of nX5 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order.

Original entry on oeis.org

52, 9393, 3268686, 1165032679, 416022303027, 148562491090605, 53052739133301878, 18945498248887912305, 6765569715455974117306, 2416032108072507755319229, 862781914811855377693247204
Offset: 1

Views

Author

R. H. Hardin Mar 09 2012

Keywords

Comments

Column 5 of A209503

Examples

			Some.solutions.for.n=4
..0..0..0..1..1....0..0..0..1..0....0..0..0..1..2....0..0..1..2..1
..1..2..3..0..4....1..2..3..1..4....1..2..3..3..1....1..2..0..0..1
..0..0..2..3..0....0..0..2..1..0....0..0..0..2..2....0..0..3..2..1
..1..2..3..4..3....1..2..1..0..2....1..2..3..0..4....1..2..2..1..3
		

Formula

Empirical: a(n) = 477*a(n-1) -39288*a(n-2) -2260566*a(n-3) +384983381*a(n-4) -7839029495*a(n-5) -822053991299*a(n-6) +43393443747057*a(n-7) -53028569481265*a(n-8) -43276863451172253*a(n-9) +861144708089830407*a(n-10) +12560105152201255943*a(n-11) -585547801427750429166*a(n-12) +1844814503928137349186*a(n-13) +169864312213397374809277*a(n-14) -1973425862832147661396693*a(n-15) -22712149774470250087869011*a(n-16) +523193464190926642340571533*a(n-17) +441660411868197024689408971*a(n-18) -72399044493040737831695861121*a(n-19) +297551907214542585886034744663*a(n-20) +5713832787499212458827821059861*a(n-21) -46623259772377465885556624035474*a(n-22) -237243127369110412124411695755424*a(n-23) +3524288981199833800362989098628637*a(n-24) +2017734872801406397171062873724219*a(n-25) -156854633713526170888417297289745006*a(n-26) +288740996321513734985376260993770412*a(n-27) +4248512257074452536352894145685116586*a(n-28) -15558777700629399566840752611585815096*a(n-29) -67069738645589682614836431998415986788*a(n-30) +391870580432283425810055509088818912984*a(n-31) +490477395685384136760468327177713204016*a(n-32) -5697674243306888319078564075420176168448*a(n-33) +1361972893213400216153081399915764209600*a(n-34) +49110417732470688323529968632616447403744*a(n-35) -57738853379778133440382246813990370347872*a(n-36) -239856563637438171277726574554616022449088*a(n-37) +473017651642156450864795051620927552310080*a(n-38) +565918982815415026472879163566265178445952*a(n-39) -1819274946494505618865129339183971184558080*a(n-40) -226770607406789393605631461901849446354176*a(n-41) +3439734464827697349267449602775539202958336*a(n-42) -1296196371235359346225463517905877093691392*a(n-43) -3102116320122327741128067294181852703551488*a(n-44) +2098262472225405871792913745858951958351872*a(n-45) +1180187397994592582735155882747328524566528*a(n-46) -1184748819500496796930575454944900028465152*a(n-47) -79179660215887860751640606150050469117952*a(n-48) +239377682403623686315699650654596059103232*a(n-49) -28581873174380158870112209651115589894144*a(n-50) -7808363148432063893510398863396858494976*a(n-51) for n>52

A209501 Number of nX6 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order.

Original entry on oeis.org

202, 133380, 137627625, 142937856372, 148562491090605, 154401817037192112, 160472621147386212721, 166781889837814691670272, 173339279726971874626160091, 180154479333345761550673106264
Offset: 1

Views

Author

R. H. Hardin Mar 09 2012

Keywords

Comments

Column 6 of A209503

Examples

			Some.solutions.for.n=4
..0..1..0..2..0..1....0..1..0..2..3..0....0..1..0..1..2..3....0..1..0..1..0..0
..0..2..0..1..1..3....0..2..0..4..4..4....0..2..0..4..4..4....0..2..0..3..1..2
..0..1..0..2..4..3....0..1..0..1..3..1....0..1..0..1..2..3....0..1..0..1..4..1
..0..2..0..1..2..3....0..2..0..2..1..4....0..2..0..4..2..4....0..2..0..4..0..4
		

A209502 Number of nX7 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order.

Original entry on oeis.org

855, 1920126, 5801378991, 17538444837670, 53052739133301878, 160472621147386212721, 485400266057664024464791, 1468244769479038501500597043, 4441166748603271019044231589770
Offset: 1

Views

Author

R. H. Hardin Mar 09 2012

Keywords

Comments

Column 7 of A209503

Examples

			Some solutions for n=4
..0..0..0..0..0..0..0....0..0..0..0..0..0..0....0..0..0..1..0..1..2
..1..2..3..4..1..4..1....1..2..1..2..1..2..1....2..1..2..0..2..0..2
..4..1..2..4..3..3..3....0..0..2..3..1..3..1....3..1..3..3..0..1..0
..0..4..4..3..0..4..0....2..1..0..0..1..4..1....2..3..2..0..1..2..1
		

A209496 Number of n X n 0..4 arrays with every 2X2 subblock containing exactly one value repeat, and new values 0..4 introduced in row major order.

Original entry on oeis.org

1, 6, 1938, 9502354, 416022303027, 154401817037192112, 485400266057664024464791
Offset: 1

Views

Author

R. H. Hardin Mar 09 2012

Keywords

Comments

Diagonal of A209503

Examples

			Some solutions for n=4
..0..0..1..0....0..1..0..0....0..0..0..1....0..1..0..2....0..0..0..0
..2..1..2..0....0..2..1..2....1..2..3..0....2..2..0..3....1..2..3..2
..1..3..1..2....2..1..0..0....2..3..1..3....0..1..2..0....2..3..0..3
..3..4..4..4....3..1..2..3....1..1..2..1....0..3..1..0....4..2..2..0
		
Showing 1-7 of 7 results.