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.

A183542 First of two complementary trees generated by the Wythoff sequences.

Original entry on oeis.org

1, 2, 5, 4, 8, 9, 16, 7, 13, 14, 24, 15, 26, 27, 45, 12, 21, 22, 37, 23, 39, 40, 66, 25, 42, 43, 71, 44, 73, 74, 121, 20, 34, 55, 58, 36, 60, 61, 100, 38, 63, 64, 105, 65, 107, 108, 176, 41, 68, 69, 113, 70, 115, 116, 189, 72, 118, 119, 194, 120, 196, 197, 320
Offset: 1

Views

Author

Clark Kimberling, Jan 05 2011

Keywords

Comments

Begin with the main tree A074049 generated by the Wythoff sequences:
...................1
...................2
...........3.................5
.......4.......7........8........13
.....6..10...11..18....12..20...21..34
Every n >2 is in the subtree from 3 or the subtree from 5. Therefore, on subtracting 2 from all entries in those subtrees, we obtain complementary trees: A183342 and A183543.

Examples

			First three levels:
...................1
.............2............3
..........4.....8......9.....16

Crossrefs

Cf. A074049, A183543, A183544,
A183079 (definition of tree generated by a sequence).

Formula

See the formulas at A074049 and A183544.

A183336 Number of n X 4 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

Original entry on oeis.org

1, 4, 7, 12, 26, 51, 97, 193, 380, 741, 1456, 2860, 5605, 10997, 21581, 42332, 83047, 162936, 319650, 627099, 1230289, 2413641, 4735192, 9289761, 18225136, 35754992, 70146009, 137616081, 269982313, 529665276, 1039124759, 2038608652, 3999447882
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2011

Keywords

Comments

Equivalent to all 1s connected only in 2 X 2 blocks.
Column 4 of A183342.

Examples

			Some solutions for 5 X 4:
..0..0..0..0....0..0..0..0....1..1..0..0....0..0..0..0....0..1..1..0
..0..0..0..0....0..0..0..0....1..1..0..0....0..1..1..0....0..1..1..0
..0..0..1..1....0..0..0..0....0..0..0..0....0..1..1..0....0..0..0..0
..0..0..1..1....0..0..1..1....0..1..1..0....0..0..0..0....1..1..0..0
..0..0..0..0....0..0..1..1....0..1..1..0....0..0..0..0....1..1..0..0

Links

Crossrefs

Cf. A183342.

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 2*a(n-3) - a(n-5).
Empirical g.f.: x*(1 + x)^2*(1 + x - x^2) / (1 - x - x^2 - 2*x^3 + x^5). - Colin Barker, Mar 27 2018

A183337 Number of n X 5 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

Original entry on oeis.org

1, 6, 13, 26, 72, 175, 407, 1005, 2450, 5893, 14318, 34780, 84221, 204245, 495483, 1201256, 2912843, 7064014, 17129250, 41536473, 100724269, 244248135, 592280544, 1436238121, 3482767494, 8445435610, 20479537209, 49661306333, 120424822297
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2011

Keywords

Comments

Equivalent to all 1s connected only in 2 X 2 blocks.
Column 5 of A183342.

Examples

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

Links

Crossrefs

Cf. A183342.

Formula

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

A183338 Number of n X 6 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

Original entry on oeis.org

1, 9, 23, 51, 175, 513, 1397, 4133, 12075, 34521, 100047, 290287, 838039, 2423841, 7016381, 20290449, 58686583, 169784637, 491117363, 1420584719, 4109370831, 11887034385, 34384871493, 99464136973, 287716480627, 832264983105
Offset: 1

Views

Author

R. H. Hardin, Jan 04 2011

Keywords

Comments

Equivalent to all 1s connected only in 2 X 2 blocks.
Column 6 of A183342.

Examples

			Some solutions for 5 X 6:
  0 0 0 0 1 1   0 0 0 0 0 0   1 1 0 0 1 1   0 1 1 0 1 1
  1 1 0 0 1 1   0 0 1 1 0 0   1 1 0 0 1 1   0 1 1 0 1 1
  1 1 0 0 0 0   0 0 1 1 0 0   0 0 0 0 0 0   0 0 0 0 0 0
  0 0 1 1 0 0   1 1 0 0 1 1   0 0 0 0 0 0   0 0 0 1 1 0
  0 0 1 1 0 0   1 1 0 0 1 1   0 0 0 0 0 0   0 0 0 1 1 0

Links

Crossrefs

Cf. A183342.

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 9*a(n-3) + 6*a(n-4) - 3*a(n-5) - 10*a(n-6) - 17*a(n-7) - 7*a(n-8) + 12*a(n-9) + 12*a(n-10) - 6*a(n-11).
Empirical g.f.: x*(1 + 8*x + 12*x^2 + x^3 - 9*x^4 - 22*x^5 - 26*x^6 + 5*x^7 + 24*x^8 + 6*x^9 - 6*x^10) / (1 - x - 2*x^2 - 9*x^3 - 6*x^4 + 3*x^5 + 10*x^6 + 17*x^7 + 7*x^8 - 12*x^9 - 12*x^10 + 6*x^11). - Colin Barker, Mar 27 2018

A183339 Number of nX7 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

Original entry on oeis.org

1, 13, 37, 97, 407, 1397, 4531, 16029, 55471, 188735, 651517, 2246015, 7712899, 26544813, 91374201, 314289321, 1081352347, 3720918175, 12801778315, 44045879629, 151549077973, 521423489151, 1794025850189, 6172623965117
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Equivalent to all 1s connected only in 2X2 blocks
Column 7 of A183342

Examples

			Some solutions for 5X7
..0..0..0..1..1..0..0....1..1..0..0..0..0..0....0..0..0..0..1..1..0
..0..0..0..1..1..0..0....1..1..0..0..1..1..0....1..1..0..0..1..1..0
..0..0..0..0..0..1..1....0..0..0..0..1..1..0....1..1..0..0..0..0..0
..1..1..0..0..0..1..1....0..0..0..0..0..0..0....0..0..1..1..0..0..0
..1..1..0..0..0..0..0....0..0..0..0..0..0..0....0..0..1..1..0..0..0

Links

Formula

Empirical: a(n)=a(n-1)+2*a(n-2)+18*a(n-3)+17*a(n-4)+7*a(n-5)-40*a(n-6)-78*a(n-7)-21*a(n-8)+88*a(n-9)+62*a(n-10)-49*a(n-11)-24*a(n-12)+9*a(n-13)-18*a(n-14)+2*a(n-15)+9*a(n-16)+4*a(n-17)+4*a(n-18)

A183340 Number of nX8 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

Original entry on oeis.org

1, 19, 63, 193, 1005, 4133, 16029, 68662, 286079, 1170324, 4869491, 20218182, 83588667, 346493199, 1436419555, 5949727953, 24653341080, 102162618558, 423291469427, 1753914307948, 7267558737304, 30113168208503, 124774750283399
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Equivalent to all 1s connected only in 2X2 blocks
Column 8 of A183342

Examples

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

Links

Formula

Empirical: a(n)=a(n-1)+4*a(n-2)+33*a(n-3)+40*a(n-4)-27*a(n-5)-190*a(n-6)-384*a(n-7)+149*a(n-8)+768*a(n-9)+398*a(n-10)-281*a(n-11)+312*a(n-12)-879*a(n-13)-1871*a(n-14)+351*a(n-15)+2551*a(n-16)-928*a(n-17)+499*a(n-18)+267*a(n-19)-947*a(n-20)-295*a(n-21)-55*a(n-22)+284*a(n-23)+192*a(n-24)+136*a(n-25)+98*a(n-26)-86*a(n-27)+17*a(n-28)-4*a(n-29)-19*a(n-30)+3*a(n-31)-12*a(n-32)

A183341 Number of nX9 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

Original entry on oeis.org

1, 28, 109, 380, 2450, 12075, 55471, 286079, 1429824, 6989477, 34856362, 173451524, 858586095, 4263159553, 21172762001, 105041615196, 521348098233, 2587930504660, 12843811121650, 63746482751185, 316398514788731
Offset: 1

Views

Author

R. H. Hardin Jan 04 2011

Keywords

Comments

Equivalent to all 1s connected only in 2X2 blocks
Column 9 of A183342

Examples

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

Links

Formula

Empirical: a(n)=a(n-1)+4*a(n-2)+66*a(n-3)+95*a(n-4)+43*a(n-5)-720*a(n-6)-1911*a(n-7)-1442*a(n-8)+3264*a(n-9)+10821*a(n-10)+19141*a(n-11)+2814*a(n-12)-66628*a(n-13)-89804*a(n-14)+31181*a(n-15)+153550*a(n-16)+92838*a(n-17)+40230*a(n-18)-70110*a(n-19)-229684*a(n-20)-107631*a(n-21)-94711*a(n-22)+28881*a(n-23)+390574*a(n-24)+124645*a(n-25)-26599*a(n-26)-25097*a(n-27)-277598*a(n-28)+259486*a(n-29)+159878*a(n-30)-12870*a(n-31)-21470*a(n-32)-444709*a(n-33)-78037*a(n-34)-123573*a(n-35)+71536*a(n-36)+64021*a(n-37)-594*a(n-38)+19314*a(n-39)-12660*a(n-40)+3610*a(n-41)+920*a(n-42)-1448*a(n-43)+704*a(n-44)-128*a(n-45)
Showing 1-7 of 7 results.

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