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.

A200801 T(n,k) is the number of n X k 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

1, 2, 2, 5, 15, 5, 15, 178, 178, 15, 51, 2614, 9880, 2614, 51, 187, 40148, 583813, 583813, 40148, 187, 715, 622645, 34679839, 132636590, 34679839, 622645, 715, 2795, 9676364, 2060918000, 30147154218, 30147154218, 2060918000, 9676364, 2795
Offset: 1

Views

Author

R. H. Hardin, Nov 22 2011

Keywords

Examples

			Table starts:
.....1...........2.................5......................15
.....2..........15...............178....................2614
.....5.........178..............9880..................583813
....15........2614............583813...............132636590
....51.......40148..........34679839.............30147154218
...187......622645........2060918000...........6852264918471
...715.....9676364......122478253815........1557479347400065
..2795...150442627.....7278777317468......354005859128023982
.11051..2339207390...432571571252989....80463441477635545163
.43947.36372631268.25707362563355693.18288865135614195620421
...
Some solutions for n=5 and k=3:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..2..0..0....0..1..1....0..0..2....2..2..0....2..2..0....2..2..0....2..1..2
..2..3..3....1..0..2....3..1..0....1..1..1....3..2..2....0..0..1....0..1..3
..2..2..0....3..2..1....3..3..0....2..2..1....3..1..3....1..1..1....1..1..2
		

Crossrefs

Main diagonal is A200794.
Columns 1..7 are A007581(n-1), A200795, A200796, A200797, A200798, A200799, A200780.

A198522 Number of n X 2 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

2, 15, 193, 3660, 81844, 1948672, 47436498, 1163606279, 28617909415, 704465305625, 17346617064022, 427184684002131, 10520398796919219, 259092051772297458, 6380839372392481249, 157145577058895542027
Offset: 1

Views

Author

R. H. Hardin Oct 26 2011

Keywords

Comments

Column 2 of A198528.

Examples

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

Crossrefs

Cf. A198528.

Formula

Empirical: a(n) = 35*a(n-1) -267*a(n-2) +246*a(n-3) +924*a(n-4) +710*a(n-5) -1736*a(n-6) -1860*a(n-7) +72*a(n-8) +1984*a(n-9) +720*a(n-10) -320*a(n-11) -512*a(n-12) for n > 14.

A198523 Number of nX3 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

5, 193, 16714, 1877316, 222590953, 26670041125, 3201911378187, 384557171168810, 46189600128813487, 5547962760669962158, 666383179391895903794, 80041410904141273707361, 9614030302463648373863365
Offset: 1

Views

Author

R. H. Hardin Oct 26 2011

Keywords

Comments

Column 3 of A198528

Examples

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

Formula

Empirical: a(n) = 140*a(n-1) -2296*a(n-2) -11502*a(n-3) +41183*a(n-4) +408760*a(n-5) +595837*a(n-6) -3718654*a(n-7) -13795951*a(n-8) -11064332*a(n-9) +29075688*a(n-10) +108107068*a(n-11) +134930012*a(n-12) -37607560*a(n-13) -266631136*a(n-14) -319325600*a(n-15) -322970496*a(n-16) -229207424*a(n-17) +130810368*a(n-18) +389159424*a(n-19) +272935936*a(n-20) +65761280*a(n-21) -8192000*a(n-22) -6356992*a(n-23) -786432*a(n-24) for n>25

A198524 Number of nX4 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

15, 3660, 1877316, 1084539825, 634586561196, 371815743708461, 217885196778717007, 127683385189755792564, 74824145653256981522691, 43847942678019724723096730, 25695476991145191912238756667
Offset: 1

Views

Author

R. H. Hardin Oct 26 2011

Keywords

Comments

Column 4 of A198528

Examples

			Some solutions for n=5
..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0
..0..1..1..0....0..1..1..0....0..1..1..0....0..1..1..0....0..1..1..0
..0..0..0..0....0..0..0..0....1..0..0..0....2..0..0..0....1..0..0..0
..2..3..2..4....2..1..3..1....2..0..3..4....3..0..1..1....1..0..1..2
..1..0..4..1....0..0..4..3....3..0..4..2....2..3..1..4....2..1..3..3
		

Formula

Empirical: a(n) = 635*a(n-1) -27578*a(n-2) -664895*a(n-3) +1075136*a(n-4) +521286483*a(n-5) +2748227094*a(n-6) -89204651105*a(n-7) -1168115845047*a(n-8) +9306591915990*a(n-9) +42304788343962*a(n-10) -261189926549682*a(n-11) +1315848767909456*a(n-12) +10954607284537534*a(n-13) -164731785495495987*a(n-14) -1080885231798070753*a(n-15) +6337772915200237725*a(n-16) +61973915198240765682*a(n-17) -174926704521799076140*a(n-18) -1769876739708372407462*a(n-19) +4724328200626189593230*a(n-20) +28925367737640459827048*a(n-21) -118508927361522008394407*a(n-22) -338291074875836070162743*a(n-23) +2078500757367505073417544*a(n-24) +3638638083258148122104563*a(n-25) -22533121425170101610868173*a(n-26) -35951981794618984423807318*a(n-27) +148059589343607187758481730*a(n-28) +304066001010912610265678504*a(n-29) -543286472115259646014984432*a(n-30) -1895168824990397488205106938*a(n-31) +515323596470817357216859317*a(n-32) +8036722529928241722905535107*a(n-33) +4658674126315217994389185485*a(n-34) -23520333887240276023055681024*a(n-35) -26120175729257847332834731016*a(n-36) +47521762151458452659065279664*a(n-37) +72064304438839106911387954831*a(n-38) -41729033682747124756817612725*a(n-39) -100063538582590874708501775431*a(n-40) -48216552248752824661323541828*a(n-41) -38770983476975500704603496326*a(n-42) +69199895034873870415739037968*a(n-43) +280771337691101112841981861706*a(n-44) +184733821531685058029799283792*a(n-45) -163201452658375838142652433035*a(n-46) -228964026785686523613364343973*a(n-47) -122774246713934304910904367423*a(n-48) -155053344320588456470407890304*a(n-49) -99882809264047288476808827105*a(n-50) +53324812803037826578664372675*a(n-51) +201914092248708392950874791566*a(n-52) +271765815346088672075249306279*a(n-53) +248628574921061669273781811996*a(n-54) +15423737680329534006814267885*a(n-55) -209896022729096662804319861750*a(n-56) -229186442003419348720426706257*a(n-57) -120121785521481771433649205077*a(n-58) -7735080728966165564636600190*a(n-59) +56375234411286047939465681488*a(n-60) +75221248919842898190277039920*a(n-61) +45192898133556559556449870260*a(n-62) +11821114684373823010990217928*a(n-63) -8505240726855879856600819878*a(n-64) -11910243027909373556607800604*a(n-65) -8302725927108486632616630296*a(n-66) -2836261104383247082262276560*a(n-67) +156712866661252193796331328*a(n-68) +927231923402821571908741120*a(n-69) +683876449064791153012081664*a(n-70) +262930466460133858491167744*a(n-71) +33590254005629207243431936*a(n-72) -30497588710990717377200128*a(n-73) -24091194787071846063800320*a(n-74) -9341232987121533770268672*a(n-75) -1964473495355240679997440*a(n-76) +68495837187683634905088*a(n-77) +232862864734779755986944*a(n-78) +109343325199815281737728*a(n-79) +32753423481532588228608*a(n-80) +7654527620812080414720*a(n-81) +1428195666470526517248*a(n-82) +202075648864951468032*a(n-83) +20776019874734407680*a(n-84) for n>85

A198525 Number of nX5 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

52, 81844, 222590953, 634586561196, 1814002928583853, 5186266567454077293, 14827770532074166305565, 42393290191915767856385826, 121204405622972228787863169567, 346529082914494875185400399625818
Offset: 1

Views

Author

R. H. Hardin Oct 26 2011

Keywords

Comments

Column 5 of A198528

Examples

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

A198526 Number of nX6 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

202, 1948672, 26670041125, 371815743708461, 5186266567454077293, 72341858272434900016248, 1009078065869144136137180812, 14075371934477934686865356966591, 196333764385468923490801365319931630
Offset: 1

Views

Author

R. H. Hardin Oct 26 2011

Keywords

Comments

Column 6 of A198528

Examples

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

A198521 Number of n X n 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

1, 15, 16714, 1084539825, 1814002928583853, 72341858272434900016248
Offset: 1

Views

Author

R. H. Hardin, Oct 26 2011

Keywords

Examples

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

Crossrefs

Diagonal of A198528.

A198527 Number of nX7 0..4 arrays with values 0..4 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

Original entry on oeis.org

855, 47436498, 3201911378187, 217885196778717007, 14827770532074166305565, 1009078065869144136137180812
Offset: 1

Views

Author

R. H. Hardin Oct 26 2011

Keywords

Comments

Column 7 of A198528

Examples

			Some solutions for n=4
..0..0..0..1..0..0..2....0..0..0..1..0..2..3....0..0..0..1..0..2..2
..1..1..0..0..2..1..3....1..1..0..0..2..4..1....1..1..0..0..2..3..0
..0..0..1..0..2..3..0....0..0..1..0..2..2..1....0..0..1..0..2..1..1
..0..0..1..0..0..3..4....0..0..1..0..0..0..4....0..0..1..0..0..0..3
		
Showing 1-8 of 8 results.