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 11 results. Next

A223784 Number of n X 3 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

22, 484, 8635, 151580, 2703137, 48302789, 862007289, 15379566078, 274427327200, 4896915028511, 87380287912506, 1559204462831053, 27822300189794631, 496458709513621497, 8858765510668046944, 158075026701646689756
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Comments

Column 3 of A223789.

Examples

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

Crossrefs

Cf. A223789.

Formula

Empirical: a(n) = 18*a(n-1) -24*a(n-2) +364*a(n-3) +605*a(n-4) -5879*a(n-5) -3267*a(n-6) -28514*a(n-7) -68422*a(n-8) +215872*a(n-9) +381625*a(n-10) +110428*a(n-11) +62650*a(n-12) -42873*a(n-13) -108576*a(n-14) -28080*a(n-15).

A223785 Number of nX4 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

46, 2116, 62365, 1560013, 39387861, 1026135371, 27088106846, 715394830136, 18858304684055, 496722962933967, 13083748459268997, 344674592599166771, 9080493561769780564, 239226142956291614446, 6302367997324565980625
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Column 4 of A223789

Examples

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

Formula

Empirical: a(n) = 36*a(n-1) -189*a(n-2) -3541*a(n-3) +59127*a(n-4) -226113*a(n-5) -2332737*a(n-6) +9857697*a(n-7) +99543550*a(n-8) +95675691*a(n-9) -5724165128*a(n-10) +5396730978*a(n-11) +117801963183*a(n-12) +48822212002*a(n-13) -4050581859555*a(n-14) -9385185579247*a(n-15) +93974968759615*a(n-16) +418814395559996*a(n-17) -398631629899971*a(n-18) -8857200756180654*a(n-19) -17297999616825626*a(n-20) +61168241169556772*a(n-21) +315463283515803651*a(n-22) +213887059257798310*a(n-23) -1903664148042753413*a(n-24) -3584708139929595584*a(n-25) +1714913055484581266*a(n-26) +11096777221831756444*a(n-27) -7609600734685922241*a(n-28) -49783583957613699145*a(n-29) +229513376763785174005*a(n-30) +180988649676924655797*a(n-31) -501542105212285553370*a(n-32) -325246768938962167438*a(n-33) +1501252528314140198120*a(n-34) +5802160737866727525882*a(n-35) -16205743701771553347998*a(n-36) -12947461293194280857390*a(n-37) -36099351841893292475137*a(n-38) +81150506478189926731033*a(n-39) +315683614302924768396043*a(n-40) -678254108759024930127839*a(n-41) -174717381067845210519994*a(n-42) +1334495710753290909569152*a(n-43) +221178153601308790024930*a(n-44) -483252100375673175449627*a(n-45) -2714447412869195417032469*a(n-46) +1574170270974397211830313*a(n-47) +753869711211526732155023*a(n-48) -5395070252732438366552504*a(n-49) +4757066470991903272143408*a(n-50) +8876390245281412619998437*a(n-51) -1877127082673826201189221*a(n-52) -12865570823541965542911108*a(n-53) +2207607579231775223357612*a(n-54) +13699987590118569137971332*a(n-55) -9938636241626662896298108*a(n-56) -16701218412807619111473012*a(n-57) +8284692714173402914397700*a(n-58) +16110317416374339328207960*a(n-59) -4384172067171970298981184*a(n-60) -6240892805930542467867088*a(n-61) +6453778250708127079582832*a(n-62) +1554531273179700190700896*a(n-63) -3413324636388770330606720*a(n-64) -34723774750877869086976*a(n-65) -189654079977746620978816*a(n-66) -1002029019037833715250176*a(n-67) -163481539387725950018304*a(n-68) +145241176478505601837056*a(n-69) +105485623837957432606720*a(n-70) +101928363962749438431232*a(n-71) +53672511863761575182336*a(n-72) +11193681570052043833344*a(n-73) +225784053502893359104*a(n-74) -316491621666724773888*a(n-75) -131089967696959242240*a(n-76) -46043707372770164736*a(n-77) -9232452487045185536*a(n-78) -858153604115070976*a(n-79) -26310763496865792*a(n-80)

A223786 Number of nX5 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

86, 7396, 334230, 11012718, 343454446, 11150023974, 377163884938, 12972494260444, 446829906314726, 15355124632228358, 526923763141934474, 18077525750169013666, 620311802079829363850, 21288659601586901388818
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Column 5 of A223789

Examples

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

A223787 Number of nX6 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

148, 21904, 1455816, 61333566, 2226551034, 82093381460, 3219192158949, 131884144499255, 5492364938094602, 229040827160337252, 9528541541617112954, 395783235818312434134, 16434316529261925355928, 682564737563907412343494
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Column 6 of A223789

Examples

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

A223788 Number of nX7 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

239, 57121, 5425943, 288823579, 11992802966, 478507693443, 20229461153969, 915762458891757, 43206434381517063, 2069374312587593444, 99272303599050335774, 4753191310090939188404, 227274223415204231413155
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Column 7 of A223789

Examples

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

A223790 Number of 3 X n 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

27, 729, 8635, 62365, 334230, 1455816, 5425943, 17876443, 53233499, 145612231, 370377451, 884526855, 1998822498, 4301425736, 8862298953, 17560558967, 33594162385, 62253768525, 112071502931, 196491932081, 336258321854
Offset: 1

Views

Author

R. H. Hardin, Mar 27 2013

Keywords

Comments

Row 3 of A223789.

Examples

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

Crossrefs

Cf. A223789.

Formula

Empirical: a(n) = (5051/239500800)*n^12 + (9539/39916800)*n^11 + (86021/21772800)*n^10 + (2861/103680)*n^9 + (1419461/7257600)*n^8 + (453883/403200)*n^7 + (30663023/21772800)*n^6 + (10887469/725760)*n^5 - (167107181/5443200)*n^4 + (16805993/129600)*n^3 - (226950043/831600)*n^2 + (1171756/3465)*n - 185 for n>1.

A223791 Number of 4Xn 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

81, 6561, 151580, 1560013, 11012718, 61333566, 288823579, 1196519547, 4468789562, 15293854291, 48524120300, 143996244303, 402491787780, 1065874328092, 2687501352957, 6479586585575, 14994608609716, 33416226803133
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Row 4 of A223789

Examples

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

Formula

Empirical: a(n) = (456419/5230697472000)*n^16 + (165527/653837184000)*n^15 + (1160527/37362124800)*n^14 + (4098907/18681062400)*n^13 - (2323961/28740096000)*n^12 + (686821469/7185024000)*n^11 - (1282316951/1828915200)*n^10 + (6465409549/914457600)*n^9 + (69811138547/5225472000)*n^8 - (199799815457/326592000)*n^7 + (10755338490607/1437004800)*n^6 - (18136370082679/359251200)*n^5 + (23466839810116957/108972864000)*n^4 - (2416825957955693/4540536000)*n^3 + (2240986165151/4324320)*n^2 + (7139372965/18018)*n - 659081 for n>8

A223792 Number of 5Xn 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

243, 59049, 2703137, 39387861, 343454446, 2226551034, 11992802966, 57005353680, 246381084601, 983376748824, 3659208824870, 12782748762891, 42154099154095, 131837732493171, 392589737558511, 1116957062770205, 3045559149318525
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Row 5 of A223789

Examples

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

Formula

Empirical: a(n) = (63370093/405483668029440000)*n^20 - (268330757/121645100408832000)*n^19 + (43030249/328326856704000)*n^18 - (5473141/17072996548608)*n^17 - (2435352473/69742632960000)*n^16 + (170082680039/62768369664000)*n^15 - (9040480367419/125536739328000)*n^14 + (52864434956213/37661021798400)*n^13 - (1853752694469833/96566722560000)*n^12 + (2309334348058723/9656672256000)*n^11 - (7549354911696211/2145927168000)*n^10 + (117446496741518107/1931334451200)*n^9 - (140966223776288630033/156920924160000)*n^8 + (91382436096707306951/9415255449600)*n^7 - (86620685132489250907/1207084032000)*n^6 + (58712885643301237303/174356582400)*n^5 - (288444549825617915291/343062720000)*n^4 + (167215711426064855461/308756448000)*n^3 - (1138388070473741029/24443218800)*n^2 + (154082848393578809/16628040)*n - 14652081349 for n>15

A223793 Number of 6Xn 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

729, 531441, 48302789, 1026135371, 11150023974, 82093381460, 478507693443, 2431894894768, 11344157673659, 49637341916982, 205245174369997, 804275933241975, 2993676733618967, 10612510462313603, 35930784248755558
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Row 6 of A223789

Examples

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

A223783 Number of n X n 0..2 arrays with rows, diagonals and antidiagonals unimodal.

Original entry on oeis.org

3, 81, 8635, 1560013, 343454446, 82093381460, 20229461153969, 5020313112266183
Offset: 1

Views

Author

R. H. Hardin Mar 27 2013

Keywords

Comments

Diagonal of A223789

Examples

			Some solutions for n=3
..2..1..1....0..1..1....0..2..1....0..0..2....0..0..0....2..1..0....0..0..1
..1..1..1....0..2..0....2..1..0....0..1..1....0..1..1....1..1..0....0..2..2
..0..1..1....2..2..1....0..2..1....0..2..2....2..1..0....2..1..0....2..1..0
		
Showing 1-10 of 11 results. Next