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.

A198648 Number of n X 1 0..6 arrays with values 0..6 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

0, 1, 1, 2, 3, 6, 11, 23, 47, 103, 226, 518, 1200, 2867, 6946, 17233, 43385, 111354, 289861, 766767, 2054605, 5579891, 15325432, 42559486, 119312586, 337469019, 961850000, 2760643085, 7971239103, 23140321458, 67486362815, 197615025815
Offset: 1

Views

Author

R. H. Hardin, Oct 28 2011

Keywords

Comments

Column 1 of A198654.

Examples

			All solutions for n=5:
..0....0....0
..0....0....0
..0....0....1
..1....0....1
..1....0....1
		

Crossrefs

Cf. A198654.

Formula

Empirical: a(n) = 6*a(n-1) +a(n-2) -60*a(n-3) +50*a(n-4) +226*a(n-5) -231*a(n-6) -416*a(n-7) +361*a(n-8) +388*a(n-9) -180*a(n-10) -144*a(n-11) for n>12.
Empirical g.f.: x^2*(1 - 5*x - 5*x^2 + 50*x^3 - 4*x^4 - 184*x^5 + 36*x^6 + 303*x^7 - 3*x^8 - 189*x^9 - 53*x^10) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 + 2*x)*(1 - 3*x)*(1 - x - x^2)*(1 - x - 3*x^2)*(1 - x - 4*x^2)). - Colin Barker, May 15 2018

A198649 Number of n X 2 0..6 arrays with values 0..6 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

1, 3, 14, 76, 488, 3521, 28030, 242849, 2264711, 22514016, 236355581, 2595953878, 29564752028, 346348460016, 4145325240330, 50411121219126, 620250713489362, 7696399884065815, 96085558605681094, 1204839099133770019
Offset: 1

Views

Author

R. H. Hardin, Oct 28 2011

Keywords

Comments

Column 2 of A198654.

Examples

			Some solutions with all values 0 to 6 for n=7
..0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..1....0..1
..1..1....1..1....0..1....1..1....1..1....1..1....1..2....0..1....0..1....0..1
..2..2....2..2....2..3....2..2....2..3....2..2....1..2....2..2....2..2....2..2
..3..4....3..3....2..3....3..4....2..3....3..3....3..3....3..4....3..3....3..4
..3..4....4..4....4..4....3..4....4..4....4..5....4..4....3..4....4..4....3..4
..5..6....5..6....5..6....5..5....5..5....4..5....5..5....5..6....5..6....5..5
..5..6....5..6....5..6....6..6....6..6....6..6....6..6....5..6....5..6....6..6
		

Crossrefs

Cf. A198654.

Formula

Empirical: a(n)=37*a(n-1)-502*a(n-2)+2817*a(n-3)-2399*a(n-4)-35852*a(n-5)+95494*a(n-6)+127482*a(n-7)-450424*a(n-8)-527274*a(n-9)+944990*a(n-10)+1784424*a(n-11)-456873*a(n-12)-2779579*a(n-13)-1492318*a(n-14)+1457417*a(n-15)+1939617*a(n-16)+390628*a(n-17)-559484*a(n-18)-375300*a(n-19)-62900*a(n-20).

A198650 Number of nX3 0..6 arrays with values 0..6 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

1, 14, 185, 3904, 98467, 3050721, 108395401, 4339928301, 188551345053, 8682042687375, 414695014034677, 20274597802217045, 1005296894185682274, 50276641088590089228, 2527391863873547297914, 127445954014211525204603
Offset: 1

Views

Author

R. H. Hardin Oct 28 2011

Keywords

Comments

Column 3 of A198654

Examples

			Some solutions with all values 0 to 6 for n=5
..0..0..1....0..0..1....0..1..2....0..1..1....0..1..1....0..0..1....0..0..0
..2..2..1....2..3..1....0..1..2....0..2..2....0..2..2....2..2..1....1..1..2
..3..4..5....2..3..3....3..3..4....3..4..5....3..3..4....3..4..5....3..3..2
..3..4..5....4..5..6....5..6..4....3..4..5....5..6..4....3..4..5....4..5..6
..6..6..5....4..5..6....5..6..4....3..6..6....5..6..4....3..6..6....4..5..6
		

Formula

Empirical: a(n) = 81*a(n-1) -821*a(n-2) -56271*a(n-3) +817404*a(n-4) +13719085*a(n-5) -161766404*a(n-6) -1839166478*a(n-7) +11363879777*a(n-8) +136010514708*a(n-9) -222894443262*a(n-10) -5199979392713*a(n-11) -6868325855133*a(n-12) +95179670938610*a(n-13) +369147874355532*a(n-14) -533026096548998*a(n-15) -6205097064740219*a(n-16) -8613391027369699*a(n-17) +42546652202736078*a(n-18) +169488793960929274*a(n-19) +26312768258696277*a(n-20) -1117495734214818564*a(n-21) -2324631994223480764*a(n-22) +1841678618579353433*a(n-23) +14678560285037056763*a(n-24) +16621475447385417884*a(n-25) -31512118736308477362*a(n-26) -108345152296982309384*a(n-27) -58218904915144342769*a(n-28) +238284037084533015029*a(n-29) +494112714724725985160*a(n-30) +83715645458904165782*a(n-31) -1046324352895906877805*a(n-32) -1682028823689223005448*a(n-33) -212054604890751854958*a(n-34) +3225128988475014814913*a(n-35) +5446552012301879705645*a(n-36) +1849700799056432967390*a(n-37) -8564584368202056735468*a(n-38) -16799593970537096861474*a(n-39) -6627276705987666615893*a(n-40) +24254079035081982103683*a(n-41) +42677642940921065893558*a(n-42) +8202157621254541156974*a(n-43) -62708452846991831276393*a(n-44) -82603416915306848302916*a(n-45) +10183617385951801505648*a(n-46) +121515459258649752469039*a(n-47) +100274939434519471128670*a(n-48) -48810733223347271082093*a(n-49) -154428754759727103485353*a(n-50) -67481826333440625909633*a(n-51) +90561617628975594540533*a(n-52) +107481511597170027775102*a(n-53) +7557656107771488311160*a(n-54) -71090863635528541203792*a(n-55) -38001596373722485470784*a(n-56) +21349925755387025519580*a(n-57) +18182235601850568334776*a(n-58) +2896440117027668706336*a(n-59) -6198133961733830403848*a(n-60) -606477045166747013360*a(n-61) +1583209521774878300176*a(n-62) -1505421146617143826080*a(n-63) +491507055481101027792*a(n-64) -28006796237834041056*a(n-65) +13190983794767505312*a(n-66) +604528701099503616*a(n-67) +407163173626382976*a(n-68) +3069878917501440*a(n-69)

A198651 Number of nX4 0..6 arrays with values 0..6 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

2, 76, 3904, 344008, 39898934, 5870175231, 996290832880, 184906809944845, 35956430134255744, 7167834458473450500, 1446698354699811336454, 293844456856748839234741, 59872951529043615795454004
Offset: 1

Views

Author

R. H. Hardin Oct 28 2011

Keywords

Comments

Column 4 of A198654

Examples

			Some solutions with all values 0 to 6 for n=4
..0..1..1..2....0..0..1..2....0..0..1..1....0..0..1..2....0..1..1..0
..0..3..4..2....3..3..1..2....2..2..1..3....0..3..1..2....0..2..2..0
..5..3..4..4....3..4..4..5....4..5..5..3....3..3..4..4....3..4..5..6
..5..6..6..6....6..6..6..5....4..6..6..3....5..5..6..6....3..4..5..6
		

A198652 Number of n X 5 0..6 arrays with values 0..6 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

3, 488, 98467, 39898934, 21787578805, 15022218265442
Offset: 1

Views

Author

R. H. Hardin, Oct 28 2011

Keywords

Comments

Column 5 of A198654.

Examples

			Some solutions with all values 0 to 6 for n=4
..0..0..1..1..2....0..0..0..1..2....0..0..1..2..2....0..0..0..0..0
..0..3..4..2..2....0..1..3..1..2....0..1..1..3..4....0..1..2..2..3
..0..3..4..5..5....2..1..3..4..4....5..6..1..3..4....4..1..5..5..3
..6..6..6..6..5....2..5..5..6..6....5..6..6..5..5....4..6..6..1..1
		

Crossrefs

Cf. A198654.

A198653 Number of nX6 0..6 arrays with values 0..6 introduced in row major order and each element equal to at least one horizontal or vertical neighbor.

Original entry on oeis.org

6, 3521, 3050721, 5870175231, 15022218265442
Offset: 1

Views

Author

R. H. Hardin Oct 28 2011

Keywords

Comments

Column 6 of A198654

Examples

			Some solutions with all values 0 to 6 for n=3
..0..0..1..1..2..2....0..1..2..2..3..3....0..0..0..1..2..2....0..0..1..2..3..3
..3..3..4..5..4..6....0..1..3..3..4..5....3..3..4..1..5..5....3..4..1..2..5..5
..6..6..4..5..4..6....3..3..6..6..4..5....2..2..4..6..6..6....3..4..4..6..6..6
		
Showing 1-6 of 6 results.