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.

A251968 Number of (n+1) X (n+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.

Original entry on oeis.org

256, 20000, 6250000, 1500625000, 922368160000, 410018473428480, 371968759094317056, 244967687215822061568, 286806250077948918890496, 248333886971163312349814784, 348300471444720308054703841536
Offset: 1

Views

Author

R. H. Hardin, Dec 12 2014

Keywords

Comments

Diagonal of A251974.

Examples

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

Links

Crossrefs

Cf. A251974.

A251969 Number of (n+1)X(2+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.

Original entry on oeis.org

1600, 20000, 250000, 1750000, 12250000, 60025000, 294122500, 1129430400, 4337012736, 13940398080, 44808422400, 125737920000, 352836000000, 889440750000, 2242131890625, 5181815925000, 11975752360000, 25758754621600
Offset: 1

Views

Author

R. H. Hardin, Dec 12 2014

Keywords

Comments

Column 2 of A251974

Examples

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

Links

Formula

Empirical: a(n) = 2*a(n-1) +16*a(n-2) -34*a(n-3) -119*a(n-4) +272*a(n-5) +544*a(n-6) -1360*a(n-7) -1700*a(n-8) +4760*a(n-9) +3808*a(n-10) -12376*a(n-11) -6188*a(n-12) +24752*a(n-13) +7072*a(n-14) -38896*a(n-15) -4862*a(n-16) +48620*a(n-17) -48620*a(n-19) +4862*a(n-20) +38896*a(n-21) -7072*a(n-22) -24752*a(n-23) +6188*a(n-24) +12376*a(n-25) -3808*a(n-26) -4760*a(n-27) +1700*a(n-28) +1360*a(n-29) -544*a(n-30) -272*a(n-31) +119*a(n-32) +34*a(n-33) -16*a(n-34) -2*a(n-35) +a(n-36)
Empirical for n mod 2 = 0: a(n) = (1/195689447424)*n^18 + (17/32614907904)*n^17 + (203/8153726976)*n^16 + (377/509607936)*n^15 + (31231/2038431744)*n^14 + (239305/1019215872)*n^13 + (2108695/764411904)*n^12 + (808981/31850496)*n^11 + (47324495/254803968)*n^10 + (138392485/127401984)*n^9 + (162166271/31850496)*n^8 + (75927689/3981312)*n^7 + (84551699/1492992)*n^6 + (21804659/165888)*n^5 + (3221599/13824)*n^4 + (65735/216)*n^3 + (3305/12)*n^2 + 154*n + 40
Empirical for n mod 2 = 1: a(n) = (1/195689447424)*n^18 + (17/32614907904)*n^17 + (1627/65229815808)*n^16 + (337/452984832)*n^15 + (252719/16307453952)*n^14 + (650633/2717908992)*n^13 + (139013113/48922361856)*n^12 + (108024043/4076863488)*n^11 + (6416896093/32614907904)*n^10 + (2123295587/1811939328)*n^9 + (183000365333/32614907904)*n^8 + (29276989709/1358954496)*n^7 + (3220556174161/48922361856)*n^6 + (1287371473955/8153726976)*n^5 + (526642267375/1811939328)*n^4 + (179477108125/452984832)*n^3 + (909776415625/2415919104)*n^2 + (29884946875/134217728)*n + (16544390625/268435456)

A251970 Number of (n+1)X(4+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.

Original entry on oeis.org

40000, 1750000, 76562500, 1500625000, 29412250000, 345888060000, 4067643585600, 33470895790080, 275417656786944, 1738925256499200, 10979183698560000, 56483045388000000, 290580293025000000
Offset: 1

Views

Author

R. H. Hardin, Dec 12 2014

Keywords

Comments

Column 4 of A251974

Examples

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

Links

Formula

Empirical for n mod 2 = 0: a(n) = (1/1662081589978752614400)*n^30 + (11/92337866109930700800)*n^29 + (943/83104079498937630720)*n^28 + (47953/69253399582448025600)*n^27 + (351019/11542233263741337600)*n^26 + (1181903/1154223326374133760)*n^25 + (237977021/8656674947806003200)*n^24 + (871812367/1442779157967667200)*n^23 + (23980946683/2164168736951500800)*n^22 + (6888391429/40077198832435200)*n^21 + (410890073857/180347394745958400)*n^20 + (469036933181/18034739474595840)*n^19 + (34778169875659/135260546059468800)*n^18 + (49833698053129/22543424343244800)*n^17 + (560393123760047/33815136514867200)*n^16 + (611489881425653/5635856085811200)*n^15 + (174883489382521/281792804290560)*n^14 + (1091661732017293/352241005363200)*n^13 + (10689328634913073/792542262067200)*n^12 + (1122700571624951/22015062835200)*n^11 + (8262098206990751/49533891379200)*n^10 + (1936285038107993/4127824281600)*n^9 + (14335680552163/12740198400)*n^8 + (340108128733/149299200)*n^7 + (38196515411/9953280)*n^6 + (1215850999/230400)*n^5 + (996397801/172800)*n^4 + (1732123/360)*n^3 + 2877*n^2 + (3290/3)*n + 200
Empirical for n mod 2 = 1: a(n) = (1/1662081589978752614400)*n^30 + (11/92337866109930700800)*n^29 + (755/66483263599150104576)*n^28 + (96137/138506799164896051200)*n^27 + (5643637/184675732219861401600)*n^26 + (95327689/92337866109930700800)*n^25 + (3084026953/110805439331916840960)*n^24 + (14195232967/23084466527482675200)*n^23 + (6285606168799/554027196659584204800)*n^22 + (1818323341547/10259762901103411200)*n^21 + (437381284243303/184675732219861401600)*n^20 + (1259711797335533/46168933054965350400)*n^19 + (150997718345688499/554027196659584204800)*n^18 + (43773380747151701/18467573221986140160)*n^17 + (1994221212754510117/110805439331916840960)*n^16 + (1379281874698406689/11542233263741337600)*n^15 + (128194112142692914747/184675732219861401600)*n^14 + (65109099544047901109/18467573221986140160)*n^13 + (25976938716966335630849/1662081589978752614400)*n^12 + (2783881569199717975213/46168933054965350400)*n^11 + (335060423413374542064199/1662081589978752614400)*n^10 + (160839481936796469771881/277013598329792102400)*n^9 + (87990300630403205261087/61558577406620467200)*n^8 + (4580647671213936778057/1538964435165511680)*n^7 + (4243423147407000686647/820781032088272896)*n^6 + (111714413920756533355/15199648742375424)*n^5 + (28125244339036387375/3377699720527872)*n^4 + (2034213950902854875/281474976710656)*n^3 + (5078568035210551875/1125899906842624)*n^2 + (1014269878926871875/562949953421312)*n + (389325925610015625/1125899906842624)

A251971 Number of (n+1)X(5+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.

Original entry on oeis.org

160000, 12250000, 937890625, 29412250000, 922368160000, 16270574342400, 287012931399936, 3373866295640064, 39660142577319936, 344307200786841600, 2989082761932960000, 20503345475844000000, 140640861824100000000
Offset: 1

Views

Author

R. H. Hardin, Dec 12 2014

Keywords

Comments

Column 5 of A251974

Examples

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

Links

A251972 Number of (n+1) X (6+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.

Original entry on oeis.org

490000, 60025000, 7353062500, 345888060000, 16270574342400, 410018473428480, 10332465530397696, 167006381634183168, 2699368454168838144, 31245878471405875200, 361679014193888160000, 3225176243350261200000
Offset: 1

Views

Author

R. H. Hardin, Dec 12 2014

Keywords

Comments

Column 6 of A251974.

Examples

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

Links

Crossrefs

Cf. A251974.

A251973 Number of (n+1)X(7+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column.

Original entry on oeis.org

1500625, 294122500, 57648010000, 4067643585600, 287012931399936, 10332465530397696, 371968759094317056, 8266815890892066816, 183725765411866546176, 2835563471280083174400, 43763160717460467360000
Offset: 1

Views

Author

R. H. Hardin, Dec 12 2014

Keywords

Comments

Column 7 of A251974

Examples

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

Links

Showing 1-6 of 6 results.

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