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.

A250966 Number of (n+1)X(n+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

14, 308, 22048, 5089900, 3794909318, 9135168475316, 71001116832347962, 1781714118279963697630, 144355770055582148091515150, 37761829882206405363232456330430, 31892938416369811765366547510541575588
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Diagonal of A250973

Examples

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

A250967 Number of (n+1) X (2+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

49, 308, 1945, 12281, 77537, 489543, 3090834, 19514643, 123209858, 777911692, 4911511266, 31009873218, 195787443967, 1236145757310, 7804669708967, 49276445682891, 311117342524943, 1964305653103961, 12402062409962968
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Examples

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

Crossrefs

Column 2 of A250973.

Formula

Empirical: a(n) = 8*a(n-1) - 13*a(n-2) + 17*a(n-3) - 14*a(n-4) + 3*a(n-5).
Empirical g.f.: x*(49 - 84*x + 118*x^2 - 108*x^3 + 24*x^4) / ((1 - x)*(1 - 7*x + 6*x^2 - 11*x^3 + 3*x^4)). - Colin Barker, Nov 24 2018

A250968 Number of (n+1)X(3+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

172, 1945, 22048, 249921, 2833397, 32124018, 364210219, 4129278507, 46816221866, 530784935436, 6017842440934, 68228062145830, 773544424316648, 8770159340495832, 99432808820402153, 1127332250873994176
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 3 of A250973

Examples

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

Formula

Empirical: a(n) = 16*a(n-1) -68*a(n-2) +210*a(n-3) -492*a(n-4) +705*a(n-5) -675*a(n-6) +389*a(n-7) -120*a(n-8) +20*a(n-9)

A250969 Number of (n+1)X(4+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

604, 12281, 249921, 5089900, 103684186, 2112130109, 43025963570, 876479703950, 17854730951799, 363717955042320, 7409282841342444, 150934183848595064, 3074673806193093731, 62634048639412217021, 1275915526747412367745
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 4 of A250973

Examples

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

Formula

Empirical: a(n) = 32*a(n-1) -322*a(n-2) +2227*a(n-3) -12086*a(n-4) +47762*a(n-5) -142463*a(n-6) +321616*a(n-7) -516143*a(n-8) +570208*a(n-9) -437734*a(n-10) +223620*a(n-11) -61118*a(n-12) +2048*a(n-13) -581*a(n-14) +2307*a(n-15) -712*a(n-16) +60*a(n-17)

A250970 Number of (n+1)X(5+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

2121, 77537, 2833397, 103684186, 3794909318, 138900769559, 5084110136919, 186091438754901, 6811422962008298, 249315542243292284, 9125588509861083659, 334019954168148561523, 12225987350399215480885, 447502506618626972091831
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 5 of A250973

Examples

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

Formula

Empirical: a(n) = 64*a(n-1) -1446*a(n-2) +21783*a(n-3) -257090*a(n-4) +2364533*a(n-5) -17301630*a(n-6) +102437299*a(n-7) -484439145*a(n-8) +1808535109*a(n-9) -5311996643*a(n-10) +12229385847*a(n-11) -21849236431*a(n-12) +29285048520*a(n-13) -26153502129*a(n-14) +7239648236*a(n-15) +20967448076*a(n-16) -41791947829*a(n-17) +41249669536*a(n-18) -19653544893*a(n-19) -9216125179*a(n-20) +29489025257*a(n-21) -33624035531*a(n-22) +25340528985*a(n-23) -13860558578*a(n-24) +5642370770*a(n-25) -1727464741*a(n-26) +397748431*a(n-27) -68146076*a(n-28) +8635216*a(n-29) -707328*a(n-30) +35280*a(n-31)

A250971 Number of (n+1)X(6+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

7448, 489543, 32124018, 2112130109, 138900769559, 9135168475316, 600808386292820, 39514486757351514, 2598824818868706096, 170921926401546121395, 11241352463500152822391, 739331740764868834365986
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 6 of A250973

Examples

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

Formula

Empirical recurrence of order 57 (see link above)

A250972 Number of (n+1)X(7+1) 0..1 arrays with no 2X2 subblock having the sum of its diagonal elements less than the absolute difference of its antidiagonal elements.

Original entry on oeis.org

26154, 3090834, 364210219, 43025963570, 5084110136919, 600808386292820, 71001116832347962, 8390658772408694576, 991579229128088199012, 117181450181585451488011, 13848104464047186015193590
Offset: 1

Views

Author

R. H. Hardin, Nov 29 2014

Keywords

Comments

Column 7 of A250973

Examples

			Some solutions for n=1
..1..0..0..1..1..1..1..1....0..1..0..1..1..0..1..0....0..1..0..1..0..1..0..0
..1..1..1..0..1..0..1..0....1..1..1..1..0..1..1..1....0..1..0..1..1..0..0..1
		
Showing 1-7 of 7 results.