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.

A196807 Number of nX6 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 41, 420, 8719, 166682, 2535368, 46685074, 822353649, 14219232895, 247793610490, 4321118145913, 75358654335980, 1315206264464536, 22934359993226090, 399880131880385285, 6973750320639071161
Offset: 1

Views

Author

R. H. Hardin Oct 06 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's
Column 6 of A196809

Examples

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

Formula

Empirical: a(n) = 4*a(n-1) +81*a(n-2) +1187*a(n-3) +14009*a(n-4) +152601*a(n-5) +972831*a(n-6) +1112105*a(n-7) -15436914*a(n-8) -72110331*a(n-9) -142326597*a(n-10) -991340283*a(n-11) -547633934*a(n-12) +16220401435*a(n-13) +20288910387*a(n-14) +2885028194*a(n-15) +368091443331*a(n-16) -1230469139652*a(n-17) -1955748191845*a(n-18) -916989452296*a(n-19) -20894508968521*a(n-20) +102899177075844*a(n-21) +64658065178654*a(n-22) -86252448610683*a(n-23) +3995043990057793*a(n-24) -13212680295761472*a(n-25) +11723249089236806*a(n-26) -17552499231979387*a(n-27) -160267711456330981*a(n-28) +525218212810881548*a(n-29) -573999045950482216*a(n-30) -334216597215077028*a(n-31) +9603972602378184406*a(n-32) -40244536999676938658*a(n-33) +117636762994743535342*a(n-34) -300575655937989219752*a(n-35) +587416616200388511329*a(n-36) -942757838826774568207*a(n-37) +1328885545845745047126*a(n-38) -1334572810933812145830*a(n-39) +1028054676357174733785*a(n-40) -854575907062291150449*a(n-41) -1011829624515934604803*a(n-42) +4701332553608363074901*a(n-43) -6832212290502712893095*a(n-44) +7502475094241840182160*a(n-45) -6734631935365713227978*a(n-46) +11868475287395189767435*a(n-47) -27215358415341998659721*a(n-48) +22412873289397146927366*a(n-49) -16108608991801633690875*a(n-50) +56970216675059509502782*a(n-51) -43457227880491589807962*a(n-52) -36607628796861286486714*a(n-53) -2585733147078693658147*a(n-54) +41407704226336920009933*a(n-55) +52715095931971737825423*a(n-56) -6138505750133038229708*a(n-57) -103708455511843309729639*a(n-58) +30684433520799082291050*a(n-59) -30258518023038983364839*a(n-60) +73140231874272363580745*a(n-61) +42872704759446098960495*a(n-62) -52008221241581236423762*a(n-63) +7556215203773523028438*a(n-64) -87196011625060565892570*a(n-65) +38724935200198777167388*a(n-66) +39385209467687328287040*a(n-67) +20008287306966500986968*a(n-68) +3843148667954450581176*a(n-69) -40773041066419728284240*a(n-70) -7924252907590517421600*a(n-71) +5915487932709333518304*a(n-72) +9402823819578807287648*a(n-73) +4419858399723745600256*a(n-74) -3134270370848713084736*a(n-75) -2181849523161360597760*a(n-76) -66187958852564400960*a(n-77) +229799792265042353408*a(n-78) +436838529210528607232*a(n-79) +115823154907594984448*a(n-80) +69728018986375031296*a(n-81) -27799436701604930048*a(n-82) -12413139972899878912*a(n-83) +3078113712557976576*a(n-84) +2698559738789154816*a(n-85) +2357714578735861760*a(n-86) -1408084157308383232*a(n-87) -1175976409943556096*a(n-88) -612407658040852480*a(n-89) -309485038454308864*a(n-90) -67014717934862336*a(n-91) +2662830364164096*a(n-92) +610107496333312*a(n-93) +3871662258782208*a(n-94) +192094138269696*a(n-95) +266485389852672*a(n-96) -7176563195904*a(n-97) -16755002966016*a(n-98)

A196804 Number of n X 3 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 3, 16, 37, 120, 420, 1468, 4801, 15885, 53128, 178165, 594582, 1983454, 6622194, 22119691, 73864009, 246623786, 823483995, 2749775102, 9181948002, 30659615818, 102376096183, 341847401583, 1141474348346, 3811532000911, 12727199593820
Offset: 1

Views

Author

R. H. Hardin, Oct 06 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's.
Column 3 of A196809.

Examples

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

Crossrefs

Cf. A196809.

Formula

Empirical: a(n) = 2*a(n-1) +2*a(n-2) +3*a(n-3) +17*a(n-4) +3*a(n-5) -4*a(n-6).
Empirical g.f.: x*(1 + x + 8*x^2 - 4*x^3 - 12*x^4 + 4*x^5) / (1 - 2*x - 2*x^2 - 3*x^3 - 17*x^4 - 3*x^5 + 4*x^6). - Colin Barker, May 09 2018

A196805 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 7, 37, 193, 1515, 8719, 52291, 334317, 2067173, 12663609, 78727511, 488078559, 3014804713, 18665197193, 115593457951, 715253390987, 4426801402571, 27403189146691, 169608418907807, 1049766166947791, 6497692031157569
Offset: 1

Views

Author

R. H. Hardin Oct 06 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's
Column 4 of A196809

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +9*a(n-2) +82*a(n-3) +137*a(n-4) +25*a(n-5) -6*a(n-6) +79*a(n-7) -153*a(n-8) -112*a(n-9) +76*a(n-10) -160*a(n-11) +136*a(n-12) -24*a(n-13)

A196806 Number of nX5 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 17, 120, 1515, 19449, 166682, 1730105, 18344433, 186996068, 1929020093, 20000798340, 205893266832, 2122824479646, 21911879424345, 226005819417517, 2331282643796687, 24051519818547252, 248109780944578426
Offset: 1

Views

Author

R. H. Hardin Oct 06 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's
Column 5 of A196809

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +46*a(n-2) +251*a(n-3) +912*a(n-4) +3106*a(n-5) +33732*a(n-6) +134128*a(n-7) -20034*a(n-8) -567014*a(n-9) -375318*a(n-10) -6015368*a(n-11) -16173299*a(n-12) -1856398*a(n-13) -6077492*a(n-14) +115957*a(n-15) +86716000*a(n-16) +121879353*a(n-17) +143953434*a(n-18) +89210978*a(n-19) -338982089*a(n-20) +596943388*a(n-21) -937879207*a(n-22) -29192016*a(n-23) +898444015*a(n-24) -968379863*a(n-25) +1255345857*a(n-26) -1174344242*a(n-27) +285800984*a(n-28) +142375346*a(n-29) -191125798*a(n-30) +133032528*a(n-31) -51445208*a(n-32) +22658488*a(n-33) +6236280*a(n-34) -4351872*a(n-35) +1586080*a(n-36) -1187040*a(n-37) +225696*a(n-38) +24640*a(n-39) +37248*a(n-40) +13824*a(n-41)

A196808 Number of nX7 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 99, 1468, 52291, 1730105, 46685074, 1436535356, 42144649101, 1242942835600, 36966191677933, 1095659240954513, 32430161990804370, 960817109357914432, 28466699840871876758, 843388951593615572344, 24985495292021432741463
Offset: 1

Views

Author

R. H. Hardin Oct 06 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's
Column 7 of A196809

Examples

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

A196803 Number of n X n 0..4 arrays with each element x equal to the number of its horizontal and vertical neighbors equal to 4,2,3,0,1 for x=0,1,2,3,4.

Original entry on oeis.org

1, 1, 16, 193, 19449, 2535368, 1436535356, 2099296647197, 9043086011797968, 109561680407727718539
Offset: 1

Views

Author

R. H. Hardin, Oct 06 2011

Keywords

Comments

Every 0 is next to 0 4's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 1's.
Diagonal of A196809.

Examples

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

Crossrefs

Cf. A196809.
Showing 1-6 of 6 results.