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 1-9 of 9 results.

A183313 Number of n X n binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

2, 6, 43, 480, 11385, 455509, 35629548, 4963103592, 1301324910599, 621440459491278, 550719742223029437, 895987628972185952650, 2692063790042095644897446, 14888067283069842424203964441
Offset: 1

Views

Author

R. H. Hardin Jan 03 2011

Keywords

Comments

Diagonal of A183322

Examples

			Some solutions for 6X6
..0..0..0..0..0..0....0..0..0..0..0..0....1..1..0..0..0..0....0..0..0..0..0..0
..0..1..1..0..0..0....0..0..0..1..1..0....1..1..0..0..0..0....0..0..0..0..0..0
..0..1..1..1..1..1....1..1..0..1..1..0....0..0..0..0..0..1....0..0..0..1..1..0
..1..1..0..1..1..1....1..1..1..1..0..1....1..1..0..0..0..1....0..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..1..1..1....1..1..0..0..0..1....1..1..1..1..1..1
..0..1..1..1..1..1....1..1..0..1..1..0....1..1..1..1..1..1....1..1..0..1..1..1
		

A183314 Number of n X 2 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

3, 6, 13, 27, 57, 119, 250, 523, 1097, 2297, 4815, 10086, 21137, 44283, 92793, 194419, 407378, 853559, 1788481, 3747361, 7851867, 16451910, 34471669, 72228171, 151339401, 317100335, 664418698, 1392152131, 2916968489, 6111905849
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2011

Keywords

Comments

Column 2 of A183322.
Is this related to A131246?

Examples

			Some solutions for 5 X 2.
..0..0....1..1....1..1....1..1....0..1....0..0....0..0....0..1....0..0....0..0
..0..0....1..1....1..1....1..1....0..1....0..1....0..1....0..1....0..0....0..1
..1..1....0..1....0..0....0..0....0..0....0..1....0..1....0..1....1..1....0..1
..1..1....0..1....0..1....0..0....1..1....0..1....0..0....0..1....1..1....1..1
..1..1....0..0....0..1....0..0....1..1....1..1....1..1....0..0....0..1....1..1
		

Crossrefs

Formula

Empirical: a(n) = a(n-1) + 3*a(n-2) - a(n-3) - a(n-4).
Empirical g.f.: x*(3 + 3*x - 2*x^2 - x^3) / (1 - x - 3*x^2 + x^3 + x^4). - Colin Barker, Mar 27 2018

A183315 Number of n X 3 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

5, 13, 43, 124, 377, 1109, 3305, 9767, 28959, 85677, 253693, 750777, 2222308, 6577131, 19466625, 57614249, 170519517, 504678557, 1493676557, 4420766649, 13083945331, 38723960052, 114609540289, 339204648201, 1003928499625
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2011

Keywords

Comments

Column 3 of A183322.

Examples

			Some solutions for 5 X 3:
..1..1..1....0..1..1....1..1..0....1..1..0....1..1..0....1..1..1....1..1..0
..1..1..1....1..1..1....1..1..0....1..1..0....1..1..1....1..1..1....1..1..1
..0..0..0....1..1..1....0..0..0....0..1..1....1..1..1....0..0..0....0..0..1
..0..1..1....0..1..1....0..0..0....0..1..1....1..1..0....1..1..0....0..0..1
..0..1..1....0..0..1....0..1..1....0..0..1....1..1..0....1..1..1....0..1..1
		

Crossrefs

Cf. A183322.

Formula

Empirical: a(n) = a(n-1) + 9*a(n-2) - 3*a(n-3) - 21*a(n-4) + a(n-5) + 13*a(n-6) + a(n-7) - a(n-8).
Empirical g.f.: x*(5 + 8*x - 15*x^2 - 21*x^3 + 10*x^4 + 13*x^5 - x^7) / (1 - x - 9*x^2 + 3*x^3 + 21*x^4 - x^5 - 13*x^6 - x^7 + x^8). - Colin Barker, Mar 27 2018

A183316 Number of nX4 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

8, 27, 124, 480, 1975, 7833, 31428, 125103, 498825, 1985956, 7906167, 31469417, 125232138, 498389829, 1983161935, 7891800110, 31402125248, 124956937711, 497214816218, 1978508290987, 7872687718931, 31326612697486, 124652113265387
Offset: 1

Views

Author

R. H. Hardin Jan 03 2011

Keywords

Comments

Column 4 of A183322

Examples

			Some solutions for 5X4
..0..1..1..0....0..0..0..0....0..1..1..0....0..0..0..1....0..1..1..1
..0..1..1..0....0..0..0..0....0..1..1..0....0..1..1..1....0..1..1..1
..1..1..0..0....0..1..1..1....0..0..0..0....0..1..1..0....1..1..0..1
..1..1..1..1....0..1..1..1....0..0..0..0....0..0..0..0....1..1..0..1
..0..0..1..1....1..1..1..1....0..0..1..1....0..1..1..0....1..1..1..1
		

Formula

Empirical: a(n)=a(n-1)+23*a(n-2)-10*a(n-3)-180*a(n-4)+34*a(n-5)+630*a(n-6)-63*a(n-7)-1081*a(n-8)+73*a(n-9)+914*a(n-10)-50*a(n-11)-352*a(n-12)+14*a(n-13)+47*a(n-14)+a(n-15)-a(n-16)

A183317 Number of nX5 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

13, 57, 377, 1975, 11385, 61755, 343035, 1872913, 10288475, 56225061, 307755285, 1681755047, 9194060283, 50235380141, 274514218163, 1499800424044, 8194423899045, 44768307376625, 244584423489933, 1336207363455509
Offset: 1

Views

Author

R. H. Hardin Jan 03 2011

Keywords

Comments

Column 5 of A183322

Examples

			Some solutions for 5X5
..0..0..1..1..0....1..1..0..0..0....0..0..0..0..0....0..0..0..0..1
..0..0..1..1..1....1..1..0..0..0....0..0..1..1..1....0..0..0..1..1
..0..0..0..0..1....0..0..0..0..0....0..0..1..1..1....0..0..0..1..1
..0..1..1..0..0....0..0..0..1..1....0..1..1..0..1....1..1..0..0..1
..0..1..1..0..1....0..0..0..1..1....1..1..1..1..1....1..1..0..1..1
		

Formula

Empirical: a(n)=a(n-1)+61*a(n-2)-29*a(n-3)-1491*a(n-4)+297*a(n-5)+19701*a(n-6)-1185*a(n-7)-159127*a(n-8)-819*a(n-9)+836109*a(n-10)+27171*a(n-11)-2951431*a(n-12)-125221*a(n-13)+7095801*a(n-14)+329665*a(n-15)-11617381*a(n-16)-586437*a(n-17)+12793417*a(n-18)+723297*a(n-19)-9246383*a(n-20)-590475*a(n-21)+4223841*a(n-22)+294743*a(n-23)-1155939*a(n-24)-81687*a(n-25)+173913*a(n-26)+10715*a(n-27)-12215*a(n-28)-423*a(n-29)+281*a(n-30)-a(n-31)-a(n-32)

A183318 Number of nX6 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

21, 119, 1109, 7833, 61755, 455509, 3437801, 25528515, 190243099, 1412491505, 10484413673, 77772795145, 576515430247, 4273815283079, 31666450138863, 234664439146089, 1738444321229885, 12880327740810545, 95414952005019587
Offset: 1

Views

Author

R. H. Hardin Jan 03 2011

Keywords

Comments

Column 6 of A183322

Examples

			Some solutions for 5X6
..0..0..0..0..0..1....0..0..1..1..0..0....0..0..0..1..1..1....0..0..0..1..1..0
..0..1..1..0..0..1....1..1..1..1..1..1....0..0..0..1..1..1....0..1..1..1..1..1
..0..1..1..0..0..1....1..1..0..1..1..1....0..0..0..0..0..0....1..1..1..1..0..1
..0..0..0..0..0..1....0..0..1..1..0..0....0..1..1..1..1..0....1..1..1..1..0..0
..1..1..0..0..0..1....1..1..1..1..0..1....0..1..1..1..1..0....0..1..1..0..0..1
		

Formula

Empirical: a(n)=a(n-1)+155*a(n-2)-83*a(n-3)-10499*a(n-4)+2739*a(n-5)+418493*a(n-6)-42935*a(n-7)-11114743*a(n-8)+187159*a(n-9)+210582515*a(n-10)+4942581*a(n-11)-2969847775*a(n-12)-106170955*a(n-13)+32076857369*a(n-14)+1009462397*a(n-15)-270649716999*a(n-16)-4937331775*a(n-17)+1809326210403*a(n-18)+1914644979*a(n-19)-9680756335999*a(n-20)+163670254649*a(n-21)+41751512005591*a(n-22)-1408662580253*a(n-23)-145837266421261*a(n-24)+7057415803719*a(n-25)+413726670171893*a(n-26)-24987326051091*a(n-27)-954307354257023*a(n-28)+66458580117683*a(n-29)+1789004571454345*a(n-30)-136365538707579*a(n-31)-2720716316400381*a(n-32)+218575487621235*a(n-33)+3345872171110277*a(n-34)-274993070105947*a(n-35)-3312136548981459*a(n-36)+271453232272799*a(n-37)+2623620146984753*a(n-38)-209286828757487*a(n-39)-1650724693067001*a(n-40)+124964898554049*a(n-41)+817527401509143*a(n-42)-57057707865601*a(n-43)-315201100152543*a(n-44)+19563658984353*a(n-45)+93322287344023*a(n-46)-4906758788153*a(n-47)-20850409285435*a(n-48)+864282086203*a(n-49)+3434976022529*a(n-50)-99411558905*a(n-51)-404036952399*a(n-52)+6269911051*a(n-53)+32355800903*a(n-54)-65276327*a(n-55)-1635520523*a(n-56)-16406321*a(n-57)+45651461*a(n-58)+790773*a(n-59)-534995*a(n-60)-5413*a(n-61)+1739*a(n-62)-a(n-63)-a(n-64)

A183319 Number of n X 7 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

34, 250, 3305, 31428, 343035, 3437801, 35629548, 360327392, 3674032121, 37171418048, 376812203313, 3809267878552, 38525903428706, 389213738128583, 3932484616050161, 39713438364928384, 401069370226611064, 4049515179562143177, 40887644784074526836, 412792720508937690701
Offset: 1

Views

Author

R. H. Hardin, Jan 03 2011

Keywords

Examples

			Some solutions for 5 X 7:
..0..0..1..1..0..0..0....0..1..1..0..0..0..0....1..1..0..0..0..0..0
..1..1..1..1..0..0..0....0..1..1..0..0..0..0....1..1..0..1..1..0..0
..1..1..1..1..0..0..1....1..1..0..0..0..1..1....0..0..0..1..1..0..0
..0..0..1..1..1..1..1....1..1..0..0..1..1..1....1..1..0..0..0..0..0
..1..1..0..0..1..1..0....0..0..0..1..1..0..1....1..1..0..1..1..0..1
		

Crossrefs

Column 7 of A183322.

A183320 Number of nX8 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

55, 523, 9767, 125103, 1872913, 25528515, 360327392, 4963103592, 68795107993, 947461430557, 13049865962515, 179449989707905, 2465460224449227, 33861928082629563, 464723391441659251, 6377980328407833025
Offset: 1

Views

Author

R. H. Hardin Jan 03 2011

Keywords

Comments

Column 8 of A183322

Examples

			Some solutions for 5X8
..0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..0....0..0..0..0..0..0..0..0
..0..0..0..0..0..1..1..1....0..0..0..0..0..0..0..1....0..0..0..0..0..0..0..0
..1..1..0..0..0..1..1..1....0..1..1..0..0..0..1..1....0..0..0..0..0..0..0..1
..1..1..1..1..1..1..0..1....0..1..1..0..0..1..1..0....0..0..0..1..1..0..1..1
..1..1..1..1..1..1..1..1....0..1..1..1..1..1..1..1....0..1..1..1..1..1..1..0
		

A183321 Number of nX9 binary arrays with an element zero only if there are an even number of ones to its left and an even number of ones above it.

Original entry on oeis.org

89, 1097, 28959, 498825, 10288475, 190243099, 3674032121, 68795107993, 1301324910599, 24374459510955, 457521652409443, 8556633331945529, 160077250226203655, 2989991870865523923, 55846494235069318769
Offset: 1

Views

Author

R. H. Hardin Jan 03 2011

Keywords

Comments

Column 9 of A183322

Examples

			Some solutions for 5X9
..0..1..1..0..0..0..0..0..0....0..0..0..0..0..0..0..0..0
..0..1..1..0..0..0..0..0..0....0..0..0..0..0..0..0..0..0
..0..0..0..0..0..0..1..1..0....1..1..1..1..0..0..1..1..1
..0..0..0..0..1..1..1..1..1....1..1..1..1..0..0..1..1..1
..0..1..1..0..1..1..1..1..1....0..0..0..1..1..0..0..0..0
		
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