A068239 -id:A068239 - cp's OEIS frontend

A068256 1/6 the number of colorings of an n X n square array with 6 colors.

1, 105, 194485, 6354787485, 3662978221194885, 37246546285522069805565, 6681224184095576349599961437005, 21141920893108925844961568245788270386085, 1180188030501408210062775052100916976604905321333565, 1162187850685436026547128866816039344195930156602955871508107885

Offset: 1

R. H. Hardin, Feb 24 2002

nonn

Jean-François Alcover, Table of n, a(n) for n = 1..13

Main diagonal of A222281.

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

A222281 = Cases[Import["https://oeis.org/A222281/b222281.txt", "Table"], {, }][[All, 2]];
a[n_] := A222281[[2 n^2 - 2 n + 1]];
Table[a[n], {n, 1, 13}] (* Jean-François Alcover, Sep 23 2019 *)

a(8)-a(10) from Alois P. Heinz, Apr 27 2012

A068257 1/7 the number of colorings of an n X n square array with 7 colors.

Original entry on oeis.org

1, 186, 923526, 122408393436, 433110977725751106, 40908457493732914322944536, 103146129375410533061371714364918916, 6942544711174164051575906086886643368922134556, 12474132532762777585883439690925675118905860580968258566406

Offset: 1

R. H. Hardin, Feb 24 2002

nonn

Jean-François Alcover, Table of n, a(n) for n = 1..13

Main diagonal of A222340.

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

A222340 = Cases[Import["https://oeis.org/A222340/b222340.txt", "Table"], {, }][[All, 2]];
a[n_] := A222340[[2 n^2 - 2 n + 1]];
Table[a[n], {n, 1, 13}] (* Jean-François Alcover, Sep 23 2019 *)

a(7)-a(9) from Alois P. Heinz, Apr 27 2012

A068258 1/8 the number of colorings of an n X n square array with 8 colors.

Original entry on oeis.org

1, 301, 3418807, 1465295106499, 23698346512668445387, 14462834689097706163375677127, 333066712033498255371201983520013525951, 289435280548175417311368841643540798029239265418611, 9491047284937011500293532002379383630495589849878668222747216079

Offset: 1

R. H. Hardin, Feb 24 2002

nonn

Jean-François Alcover, Table of n, a(n) for n = 1..12

Main diagonal of A222462.

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

A222462 = Cases[Import["https://oeis.org/A222462/b222462.txt", "Table"], {, }][[All, 2]];
a[n_] := A222462[[2 n^2 - 2 n + 1]];
Table[a[n], {n, 1, 12}] (* Jean-François Alcover, Sep 23 2019 *)

a(6)-a(9) from Alois P. Heinz, Apr 27 2012

A068240 1/2 the number of colorings of a 4 X 4 square array with n colors.

Original entry on oeis.org

1, 3906, 3000366, 414425080, 19064362455, 428429377026, 5861180425996, 55823546748096, 403783634784285, 2353615149832210, 11531349080992026, 48981767072238936, 184656623163700051, 629125059062885490, 1964980839044519640, 5691311662142685376

Offset: 2

R. H. Hardin, Feb 24 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

a:= n-> n*(n-1)*(17493+(-94782+(251492+(-430857+(529770+(-492434 +(355622+(-202160+(90723+(-31939+(8675+(-1762+(253 +(-23+n)*n)*n) *n)*n)*n)*n) *n)*n) *n)*n) *n)*n)*n) /2:
seq(a(n), n=2..30); # Alois P. Heinz, Apr 27 2012

From Alois P. Heinz, Apr 27 2012 (Start)
G.f.: -(2507986*x^14 +349887529*x^13 +12282125725*x^12 +158263444274*x^11 +896159384816*x^10 +2455337616143*x^9 +3417678462327*x^8 +2453922059100*x^7 +895941969162*x^6 +158666067383*x^5 +12424532171*x^4 +363949394*x^3 +2934100*x^2 +3889*x+1)*x^2 / (x-1)^17.
a(n) = n*(n-1)*(n^14 -23*n^13 +253*n^12 -1762*n^11 +8675*n^10 -31939*n^9 +90723*n^8 -202160*n^7 +355622*n^6 -492434*n^5 +529770*n^4 -430857*n^3 +251492*n^2 -94782*n +17493)/2.
(End)

A068241 1/2 the number of colorings of a 5 X 5 square array with n colors.

Original entry on oeis.org

1, 290493, 10221446382, 25410195205090, 10988934663584655, 1515888422040128871, 94793386050673781548, 3330373652089796835972, 75543449548467802433805, 1216257376373886871239985, 14865437328242111405302266, 144907139188443182894343078

Offset: 2

R. H. Hardin, Feb 24 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

a:= n-> n*(n-1)*(-32126211 +(258309564 +(-1033880579 +(2734090327 +(-5348136944 +(8212654097 +(-10260465459 +(10671809555 +(-9383152441 +(7046057296 +(-4548768800 +(2534102852 +(-1219915634 +(507043269 +(-181400963 +(55554975 +(-14442408 +(3148503 +(-565677 +(81675 +(-9123+(741 +(-39+n)*n) *n)*n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)*n) *n)*n)/2:
seq(a(n), n=2..30); # Alois P. Heinz, Apr 27 2012

From Alois P. Heinz, Apr 27 2012 (Start)
G.f.: (64045717133*x^23 +99613598986379*x^22 +30122616672179057*x^21 +2905816841816465011*x^20 +116885162434957285435*x^19 +2301461202426082443493*x^18 +24565180390104215669199*x^17 +152051416127748639010437*x^16 +570955972331169762888066*x^15 +1339611184016759341097870*x^14 +1999028208566595454861898*x^13 +1912423825883782158177854*x^12 +1171838449935804166262422*x^11 +455354414964383806296586*x^10 +109981844564513940260830*x^9 +15982890606970244203818*x^8 +1330217331928452928929*x^7 +58885777127277221367*x^6 +1238407862810793461*x^5 +10331590803059615*x^4 +25144532006783*x^3 +10213893889*x^2 +290467*x+1)*x^2 / (x-1)^26.
a(n) = n*(n-1)*(n^23 -39*n^22 +741*n^21 -9123*n^20 +81675*n^19 -565677*n^18 +3148503*n^17 -14442408*n^16 +55554975*n^15 -181400963*n^14 +507043269*n^13 -1219915634*n^12 +2534102852*n^11 -4548768800*n^10 +7046057296*n^9 -9383152441*n^8 +10671809555*n^7 -10260465459*n^6 +8212654097*n^5 -5348136944*n^4 +2734090327*n^3 -1033880579*n^2 +258309564*n -32126211)/2.
(End)

A068242 1/2 the number of colorings of a 6 X 6 square array with n colors.

Original entry on oeis.org

1, 50798448, 190026633752982, 16460573816989545700, 111739638856566209416695, 143179601228065200130305876, 57851338756390824653502708508, 10086461440383360741777407234232, 929834945885124428238498952273725, 52047326332129638504907000521132040

Offset: 2

R. H. Hardin, Feb 24 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 2..1000
Alois P. Heinz, G.f. for A068242

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

More terms from Alois P. Heinz, Apr 27 2012

A068243 1/2 the number of colorings of a 7 X 7 square array with n colors.

Original entry on oeis.org

1, 20934997854, 19278946338342653286, 112656664890078627543093640, 20043672552286729048799884311015, 361011452813936865714801000277216206, 1332266848133993021484807934080054103804, 1550797305138088176220498521209275420942656

Offset: 2

R. H. Hardin, Feb 24 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 2..1000
Alois P. Heinz, Formula for a(n)

Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.

More terms from Alois P. Heinz, Apr 27 2012

A068246 1/6 the number of colorings of a 5 X 5 rhombic hexagonal array with n colors.

Original entry on oeis.org

1, 672384, 24673292910, 47694893373440, 16222878355401375, 1842996126472816896, 98798500424990038764, 3068393771393664491520, 62960689342002146953005, 933100311834971308336000, 10639781338324232990590266, 97779035968707368095801344, 750090455889142956720814955

Offset: 3

R. H. Hardin, Feb 24 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 3..1000

Cf. A068239-A068305, A000332, A002417, A027441, A212162, A212163.

a:= n-> (3008737472+ (-26856982336+ (115567646848+ (-319382723824+ (636837385892+ (-975405045160+ (1192546680096+ (-1193738274422+ (995467197535+ (-699933854941+ (418375982241+ (-213720456031+ (93568827565+ (-35133626327+ (11298632622+
(-3101089711+ (722137763+ (-141421592+ (23000726+ (-3051871+ (321994+ (-25992+ (1508+(-56+n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n) *n/6:
seq (a(n), n=3..40); #  Alois P. Heinz, May 02 2012

G.f.: (1155805517421*x^22 +898154715023598*x^21 +153334491715682431*x^20 +9260621966248364140*x^19 +250086793798293779695*x^18 +3463005755473293705486*x^17 +26809839147864527991573*x^16 +122805799859998392511056*x^15 +345417237429621912129330*x^14 +610511151468783633149340*x^13 +686259871966584143669766*x^12 +491767778082675626596168*x^11 +223082415423639038320846*x^10 +62970879259692393145420*x^9 +10739574336476388551610*x^8 +1057138433525073018576*x^7 +56029398700931117553*x^6 +1436637989069258166*x^5 +14990828199704235*x^4 +47053606279980*x^3 +24655811251*x^2+672358*x+1)*x^3 / (x-1)^26. - Alois P. Heinz, May 02 2012

Extended beyond a(10) by Alois P. Heinz, May 02 2012

A068247 1/6 the number of colorings of a 6 X 6 rhombic hexagonal array with n colors.

Original entry on oeis.org

1, 123273728, 606966551329230, 42294602754348892160, 221621345837018832499375, 227499859288036192921814016, 76749554391225308000690033388, 11559255542512176814494743592960, 945121787128699657370828476884045, 47886238054762718784097603771840000

Offset: 3

R. H. Hardin, Feb 24 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 3..1000
Alois P. Heinz, Formula for A068247

Cf. A068239-A068305, A000332, A002417, A027441, A212162, A212163.

a(n) = A212163(n,6)/6. - Alois P. Heinz, Dec 20 2012

Extended beyond a(7) by Alois P. Heinz, May 02 2012

A068249 1/6 the number of colorings of a 6 X 6 staggered hexagonal array with n colors.

Original entry on oeis.org

1, 123933504, 607054532700510, 42295002762341131520, 221621606435023540827375, 227499908955471802467974016, 76749558468512064584917217484, 11559255724071428199019433809920, 945121792213234612017996840421965, 47886238153764555711259823337784000

Offset: 3

R. H. Hardin, Feb 24 2002

nonn

Alois P. Heinz, Table of n, a(n) for n = 3..1000
Alois P. Heinz, Formula for A068249

Cf. A068239-A068305, A000332, A002417, A027441, A212194, A212195.

Extended beyond a(7) by Alois P. Heinz, May 03 2012

cp's OEIS Frontend

A068256 1/6 the number of colorings of an n X n square array with 6 colors.

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A068257 1/7 the number of colorings of an n X n square array with 7 colors.

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A068258 1/8 the number of colorings of an n X n square array with 8 colors.

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A068240 1/2 the number of colorings of a 4 X 4 square array with n colors.

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A068241 1/2 the number of colorings of a 5 X 5 square array with n colors.

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Maple

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A068242 1/2 the number of colorings of a 6 X 6 square array with n colors.

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A068243 1/2 the number of colorings of a 7 X 7 square array with n colors.

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A068246 1/6 the number of colorings of a 5 X 5 rhombic hexagonal array with n colors.

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Author

Keywords

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Programs

Maple

Formula

Extensions

A068247 1/6 the number of colorings of a 6 X 6 rhombic hexagonal array with n colors.

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Author

Keywords

Links

Crossrefs

Formula

Extensions

A068249 1/6 the number of colorings of a 6 X 6 staggered hexagonal array with n colors.

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