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 1-10 of 10 results.

A241323 Number of nX2 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 8, 85, 1030, 13011, 165924, 2121033, 27129985, 347071157, 4440219758, 56806066313, 726751710350, 9297746189765, 118951351657555, 1521812314158867, 19469410910818078, 249083253366686135, 3186663809907191548
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Column 2 of A241328

Examples

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

Formula

Empirical: a(n) = 17*a(n-1) -57*a(n-2) +43*a(n-3) -37*a(n-4) +109*a(n-5) -62*a(n-6) -48*a(n-8) +36*a(n-9) for n>10

A241324 Number of nX3 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

2, 59, 2344, 95144, 3875244, 157912026, 6435036610, 262234101215, 10686305830308, 435477843275035, 17746165666239258, 723174326871008607, 29470090437788760318, 1200936203282125872968, 48939373545548944414862
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Column 3 of A241328

Examples

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

Formula

Empirical: a(n) = 45*a(n-1) -171*a(n-2) -57*a(n-3) -1321*a(n-4) +2701*a(n-5) +10837*a(n-6) +5209*a(n-7) +13262*a(n-8) -1578*a(n-9) -7272*a(n-10) -5706*a(n-11) -17487*a(n-12) -2511*a(n-13) +4779*a(n-14) -729*a(n-15)

A241325 Number of nX4 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

5, 530, 68935, 8949808, 1162535788, 151022716125, 19619065042282, 2548674277117248, 331093294165744259, 43011682813264944327, 5587563659405034428031, 725869475605161121443285
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Column 4 of A241328

Examples

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

Formula

Empirical recurrence of order 53 (see link above)

A241326 Number of nX5 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

14, 4877, 2034543, 842185933, 348722168314, 144410575985227, 59802363257355728, 24764963195538835763, 10255505002983178027401, 4246942838826924899875284, 1758716267127474136237141337
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Column 5 of A241328

Examples

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

A241327 Number of nX6 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

41, 45057, 60066019, 79254376889, 104609549355169, 138095118530911728, 182299462522915741748, 240653648937251996398823, 317687073439565072412214593, 419378959685869736234929351013
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Column 6 of A241328

Examples

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

A241329 Number of 2 X n 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

2, 8, 59, 530, 4877, 45057, 416533, 3851085, 35606121, 329205872, 3043762177, 28141931363, 260193887579, 2405693427789, 22242493569775, 205649030142198, 1901384099152245, 17579764368539693, 162538497819201097
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Examples

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

Crossrefs

Row 2 of A241328.

Formula

Empirical: a(n) = 12*a(n-1) - 26*a(n-2) + 2*a(n-3) + 28*a(n-4) - 6*a(n-5) - 9*a(n-6) for n>8.
Empirical g.f.: x*(2 - 16*x + 15*x^2 + 26*x^3 - 21*x^4 - 17*x^5 + 5*x^6 + 3*x^7) / ((1 - x)*(1 - x - x^2)*(1 - 10*x + 6*x^2 + 9*x^3)). - Colin Barker, Oct 29 2018

A241330 Number of 3Xn 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

5, 85, 2344, 68935, 2034543, 60066019, 1773370241, 52356524981, 1545760698649, 45636645554004, 1347364712395962, 39779252976746762, 1174432544392935470, 34673647645893709738, 1023695951556996550068, 30223338828856554979455
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Row 3 of A241328

Examples

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

Formula

Empirical: a(n) = 31*a(n-1) -26*a(n-2) -530*a(n-3) +271*a(n-4) +1431*a(n-5) +437*a(n-6) +157*a(n-7) -438*a(n-8) -846*a(n-9) -243*a(n-10) -243*a(n-11) for n>13

A241331 Number of 4Xn 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

15, 1030, 95144, 8949808, 842185933, 79254376889, 7458275852500, 701865426977495, 66049458199029896, 6215623102818695436, 584924867215713568482, 55044698604373555829472, 5180013732180082600538625
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Row 4 of A241328

Examples

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

Formula

Empirical: a(n) = 122*a(n-1) -2812*a(n-2) +16208*a(n-3) +159379*a(n-4) -2909948*a(n-5) +19694228*a(n-6) -62373244*a(n-7) -58088806*a(n-8) +1439148868*a(n-9) -5096351523*a(n-10) -3055067884*a(n-11) +59968811184*a(n-12) -73039493422*a(n-13) -301989142269*a(n-14) +945040962120*a(n-15) -745735386949*a(n-16) -844626880720*a(n-17) +2521153036681*a(n-18) -1929013979294*a(n-19) -1045472186222*a(n-20) +1583296164696*a(n-21) +1956836924036*a(n-22) -2355373350354*a(n-23) -3690081020076*a(n-24) +7567309408680*a(n-25) -2089000784295*a(n-26) -4919238685854*a(n-27) +4312880045136*a(n-28) -566304913242*a(n-29) -920941508979*a(n-30) +911638855890*a(n-31) -424728198324*a(n-32) -322761834*a(n-33) +96291263349*a(n-34) -53052692148*a(n-35) +11321287623*a(n-36) for n>38

A241332 Number of 5Xn 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

51, 13011, 3875244, 1162535788, 348722168314, 104609549355169, 31380712101748979, 9413573643641662509, 2823880131958273083335, 847106463240283581573699, 254114667346044108988181086
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Row 5 of A241328

Examples

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

A241333 Number of 6Xn 0..3 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

187, 165924, 157912026, 151022716125, 144410575985227, 138095118530911728, 132055730959382784981, 126280562312797983331007, 120757959210267024208723561, 115476876363426327956883452444
Offset: 1

Views

Author

R. H. Hardin, Apr 19 2014

Keywords

Comments

Row 6 of A241328

Examples

			Some solutions for n=2
..0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1....0..1
..1..0....2..1....0..2....0..1....0..2....1..2....1..2....0..2....1..2....1..2
..2..3....0..0....2..0....1..2....0..1....0..1....0..2....2..0....0..2....2..1
..1..0....0..0....1..2....0..2....0..1....2..1....1..2....3..0....3..0....3..0
..2..3....0..0....1..0....1..2....1..2....1..0....2..1....3..2....1..2....1..2
..3..1....1..0....3..1....0..2....0..2....0..3....2..3....1..0....2..0....1..3
		
Showing 1-10 of 10 results.