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.

A231970 Number of (n+1)X(n+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

9, 56, 841, 43983, 6507601, 2641967397, 3036560660329, 9981109155098235, 93538123901225727364, 2480246214908598898309094, 186787722909431013956841219409, 39975590681225962593258073864460074
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Comments

Diagonal of A231977

Examples

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

A231971 Number of (n+1) X (2+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

16, 56, 169, 550, 1764, 5680, 18225, 58596, 188356, 605458, 1946025, 6255180, 20106256, 64627982, 207734569, 667725402, 2146283584, 6898841796, 22175081569, 71277802674, 229109651716, 736431677100, 2367126871209, 7608702637640
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Examples

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

Crossrefs

Column 2 of A231977.

Formula

Empirical: a(n) = 3*a(n-1) + 2*a(n-3) + 4*a(n-4) - 10*a(n-5) - 2*a(n-6) - a(n-8) + a(n-9).
Empirical g.f.: x*(16 + 8*x + x^2 + 11*x^3 - 62*x^4 - 14*x^5 + x^6 - 5*x^7 + 6*x^8) / ((1 - 3*x - x^2 + x^3)*(1 + x^2 - 3*x^4 - x^6)). - Colin Barker, Oct 01 2018

A231972 Number of (n+1)X(3+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

36, 169, 841, 4489, 24964, 136900, 741321, 4024036, 21911761, 119268241, 648771841, 3529072836, 19199427844, 104453715249, 568259668900, 3091481744121, 16818570092025, 91498158928089, 497777418977476
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Comments

Column 3 of A231977

Examples

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

Formula

Empirical: a(n) = 2*a(n-1) +8*a(n-2) +36*a(n-3) +90*a(n-4) +170*a(n-5) +66*a(n-6) -303*a(n-7) -268*a(n-8) +124*a(n-9) +40*a(n-10) -200*a(n-11) -184*a(n-12) -96*a(n-13) +57*a(n-14) +146*a(n-15) +36*a(n-16) -4*a(n-17) +22*a(n-18) -10*a(n-19) +6*a(n-20) -a(n-21)

A231973 Number of (n+1)X(4+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

81, 550, 4489, 43983, 417316, 3844551, 35366809, 328433132, 3052452001, 28290095075, 262170624676, 2431326125085, 22547805893209, 209069115157116, 1938539544264801, 17975390997067603, 166679573715753604
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Comments

Column 4 of A231977

Examples

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

Formula

Empirical: a(n) = 7*a(n-1) +148*a(n-3) +344*a(n-4) +673*a(n-5) +337*a(n-6) +11361*a(n-7) +48985*a(n-8) -97191*a(n-9) -358946*a(n-10) +417305*a(n-11) +1757105*a(n-12) -2002936*a(n-13) -7478980*a(n-14) -818162*a(n-15) +5202627*a(n-16) +2279142*a(n-17) -18922108*a(n-18) -31042348*a(n-19) -55043465*a(n-20) +23805696*a(n-21) -10999792*a(n-22) +52136816*a(n-23) +30760744*a(n-24) +21670317*a(n-25) +137708184*a(n-26) +27375080*a(n-27) +134395920*a(n-28) -103979476*a(n-29) +49936800*a(n-30) -43951872*a(n-31) -5680896*a(n-32) +5000768*a(n-33) -11970048*a(n-34) +4762496*a(n-35) +3064320*a(n-36) +9770624*a(n-37) +9022464*a(n-38) -7157760*a(n-39) +4641792*a(n-40) -3973120*a(n-41) +204800*a(n-42) +663552*a(n-43) -86016*a(n-44) -205824*a(n-45) +73728*a(n-46) -32768*a(n-48) +16384*a(n-49)

A231974 Number of (n+1)X(5+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

169, 1764, 24964, 417316, 6507601, 100540729, 1557328369, 24225988609, 376708702756, 5849616285604, 90862303037584, 1411766023575625, 21933150300008704, 340734844103850729, 5293483573712466276
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Comments

Column 5 of A231977

Examples

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

A231975 Number of (n+1)X(6+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

361, 5680, 136900, 3844551, 100540729, 2641967397, 69043343121, 1809552010404, 47496507516441, 1245162776547248, 32641634807741521, 855866713526323797, 22440792778234532100, 588379143180098326896, 15426782848212128167009
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Comments

Column 6 of A231977

Examples

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

A231976 Number of (n+1)X(7+1) 0..1 arrays with no element having a strict majority of its horizontal and vertical neighbors equal to one.

Original entry on oeis.org

784, 18225, 741321, 35366809, 1557328369, 69043343121, 3036560660329, 134086441384900, 5933816403750361, 262150807596195904, 11579543313397076809, 511643156104631950569, 22607722308771420398449
Offset: 1

Views

Author

R. H. Hardin, Nov 16 2013

Keywords

Comments

Column 7 of A231977

Examples

			Some solutions for n=2
..0..0..0..0..1..0..0..0....0..0..0..0..1..0..0..0....1..0..0..0..1..0..0..0
..1..1..0..0..1..0..0..1....0..0..0..0..1..0..1..0....0..0..0..0..1..0..0..0
..0..0..0..0..0..0..0..0....0..0..1..0..0..0..0..0....0..1..1..0..0..0..0..1
		
Showing 1-7 of 7 results.