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 1-7 of 7 results.

A234115 Number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

Original entry on oeis.org

31, 1361, 231713, 157630963, 427196005695, 4625943683805313, 200376051988817866625, 34754816964141969688314115, 24157262935852623408023272643359, 67332158893994957162261589597358347857
Offset: 1

Views

Author

R. H. Hardin, Dec 19 2013

Keywords

Comments

Diagonal of A234122

Examples

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

A234116 Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

Original entry on oeis.org

145, 1361, 12593, 116801, 1082977, 10041953, 93113761, 863396401, 8005833073, 74233997105, 688333901137, 6382568345057, 59182293086657, 548767146042305, 5088437180610625, 47182476443409233, 437498981379983185
Offset: 1

Views

Author

R. H. Hardin, Dec 19 2013

Keywords

Examples

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

Crossrefs

Column 2 of A234122.

Formula

Empirical: a(n) = 10*a(n-1) - 4*a(n-2) - 26*a(n-3) + 5*a(n-4).
Empirical g.f.: x*(145 - 89*x - 437*x^2 + 85*x^3) / (1 - 10*x + 4*x^2 + 26*x^3 - 5*x^4). - Colin Barker, Oct 12 2018

A234117 Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

Original entry on oeis.org

673, 12593, 231713, 4279065, 79003521, 1458813409, 26937444801, 497411686793, 9184935953377, 169604155276817, 3131820756402657, 57830550281200505, 1067868451774107585, 19718695887361293761, 364115043587212161409
Offset: 1

Views

Author

R. H. Hardin, Dec 19 2013

Keywords

Examples

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

Crossrefs

Column 3 of A234122.

Formula

Empirical: a(n) = 20*a(n-1) - 10*a(n-2) - 324*a(n-3) - 277*a(n-4) + 144*a(n-5).
Empirical g.f.: x*(673 - 867*x - 13417*x^2 - 11213*x^3 + 5904*x^4) / (1 - 20*x + 10*x^2 + 324*x^3 + 277*x^4 - 144*x^5). - Colin Barker, Oct 12 2018

A234118 Number of (n+1)X(4+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

Original entry on oeis.org

3127, 116801, 4279065, 157630963, 5807422543, 214027901025, 7888454356625, 290756314787875, 10716964158533127, 395017615132720993, 14560017639995412841, 536670372954048895219, 19781236893820566186079
Offset: 1

Views

Author

R. H. Hardin, Dec 19 2013

Keywords

Comments

Column 4 of A234122

Examples

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

Formula

Empirical: a(n) = 50*a(n-1) -427*a(n-2) -2748*a(n-3) +22158*a(n-4) +50476*a(n-5) -220478*a(n-6) -236864*a(n-7) +237555*a(n-8) +152850*a(n-9) -74775*a(n-10) -7956*a(n-11)

A234119 Number of (n+1)X(5+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

Original entry on oeis.org

14527, 1082977, 79003521, 5807422543, 427196005695, 31446640848897, 2315408571668225, 170502665692732079, 12556134956123911615, 924677153131389366689, 68097056429203867060865, 5014969801413653091728655
Offset: 1

Views

Author

R. H. Hardin, Dec 19 2013

Keywords

Comments

Column 5 of A234122

Examples

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

Formula

Empirical: a(n) = 104*a(n-1) -1893*a(n-2) -33284*a(n-3) +535522*a(n-4) +4829920*a(n-5) -36672922*a(n-6) -308181352*a(n-7) +266551299*a(n-8) +4516883912*a(n-9) +2174714575*a(n-10) -20675388468*a(n-11) -11598332564*a(n-12) +40919536464*a(n-13) +9741869952*a(n-14) -32943946752*a(n-15) +6233518080*a(n-16) +2468413440*a(n-17)

A234120 Number of (n+1)X(6+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

Original entry on oeis.org

67489, 10041953, 1458813409, 214027901025, 31446640848897, 4625943683805313, 680845368964238145, 100232847106041668353, 14757962542814417545441, 2173049645779146516000801, 319982366490305655551327777
Offset: 1

Views

Author

R. H. Hardin, Dec 19 2013

Keywords

Comments

Column 6 of A234122

Examples

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

Formula

Empirical: a(n) = 261*a(n-1) -18560*a(n-2) +127208*a(n-3) +23755242*a(n-4) -406238978*a(n-5) -11768024848*a(n-6) +211536189168*a(n-7) +3167620020453*a(n-8) -43174324632265*a(n-9) -498144039526280*a(n-10) +3974314857666608*a(n-11) +43883259123774428*a(n-12) -167685268616512940*a(n-13) -2040900846762609856*a(n-14) +3445445946343381888*a(n-15) +52296679884037531065*a(n-16) -35833370093864352573*a(n-17) -776126649677016939696*a(n-18) +226412171176325558120*a(n-19) +6916149301019844647706*a(n-20) -1682665179571062843826*a(n-21) -37312103086122262303664*a(n-22) +14659167338730178934224*a(n-23) +117646777156101371452739*a(n-24) -76253461020753171154783*a(n-25) -192817994631326898576392*a(n-26) +189380280584489465020224*a(n-27) +110172317785328612275008*a(n-28) -187529085888044105270592*a(n-29) +38102718853877138892864*a(n-30) +32573701148082394908672*a(n-31) -13221821267594299551744*a(n-32) -630264421714516770816*a(n-33) +672250225845986131968*a(n-34) -28475524214125756416*a(n-35)

A234121 Number of (n+1)X(7+1) 0..2 arrays with every 2X2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.

Original entry on oeis.org

313537, 93113761, 26937444801, 7888454356625, 2315408571668225, 680845368964238145, 200376051988817866625, 58999673293833047076529, 17376516489941449765539393, 5118401705337856988983612385
Offset: 1

Views

Author

R. H. Hardin, Dec 19 2013

Keywords

Comments

Column 7 of A234122

Examples

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

Formula

Empirical recurrence of order 62 (see link above)
Showing 1-7 of 7 results.