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 1-3 of 3 results.

A221821 Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

3, 31, 252, 2113, 17684, 147920, 1237439, 10351593, 86594795, 724396370, 6059833949, 50692672540, 424062286786, 3547432284249, 29675536361423, 248246446379403, 2076670068892280, 17372085836189001, 145323694322280832
Offset: 1

Views

Author

R. H. Hardin, Jan 26 2013

Keywords

Comments

Column 2 of A221824.

Examples

			Some solutions for n=3:
..0..2....1..1....1..0....2..0....0..1....1..2....1..0....1..0....0..1....2..0
..0..1....1..2....0..3....1..1....3..1....0..2....2..0....1..3....1..2....2..0
..0..3....1..0....0..2....0..2....0..1....1..0....2..1....1..0....2..0....2..0
		

Crossrefs

Cf. A221824.

Formula

Empirical: a(n) = 9*a(n-1) - 4*a(n-2) - 11*a(n-3) - 2*a(n-4) + 22*a(n-5) - 16*a(n-6) + 8*a(n-7).
Empirical g.f.: x*(3 + 4*x - 15*x^2 + 2*x^3 + 22*x^4 - 16*x^5 + 8*x^6) / (1 - 9*x + 4*x^2 + 11*x^3 + 2*x^4 - 22*x^5 + 16*x^6 - 8*x^7). - Colin Barker, Aug 11 2018

A221822 Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

6, 252, 6711, 190756, 5374720, 151592441, 4274867564, 120554575328, 3399703708400, 95873611077468, 2703690754567558, 76245627705373885, 2150170395738132532, 60636036995518426808, 1709970985328543058485
Offset: 1

Views

Author

R. H. Hardin Jan 26 2013

Keywords

Comments

Column 3 of A221824

Examples

			Some solutions for n=3
..1..3..1....0..1..0....0..2..1....1..1..1....1..0..0....2..0..1....1..1..1
..0..1..0....1..3..0....2..0..0....0..4..1....4..0..3....3..0..1....1..1..2
..0..2..1....0..3..1....1..2..1....1..0..0....0..0..1....0..2..0....0..0..2
		

Formula

Empirical: a(n) = 18*a(n-1) +312*a(n-2) -187*a(n-3) -13565*a(n-4) -20614*a(n-5) +158772*a(n-6) +381840*a(n-7) -1501245*a(n-8) -3110200*a(n-9) +13397334*a(n-10) -5218282*a(n-11) -30257641*a(n-12) +22527453*a(n-13) +59810156*a(n-14) -71002519*a(n-15) -62823023*a(n-16) +51211271*a(n-17) +211220974*a(n-18) -214821233*a(n-19) -158156578*a(n-20) +147778970*a(n-21) +223640148*a(n-22) -182698582*a(n-23) +171412*a(n-24) -59513311*a(n-25) +67158528*a(n-26) -136639431*a(n-27) +148395775*a(n-28) -84660389*a(n-29) +39605263*a(n-30) -6661260*a(n-31) +3867558*a(n-32) -132564*a(n-33) +150444*a(n-34) -5832*a(n-35)

A221823 Number of n X 4 arrays of occupancy after each element stays put or moves to some horizontal or vertical neighbor, without consecutive moves in the same direction.

Original entry on oeis.org

13, 2113, 190756, 18636989, 1804472268, 174820457922, 16936005698353, 1640717334488903, 158947987755078035, 15398437448141904936, 1491757378064714004413, 144517269678468770214198
Offset: 1

Views

Author

R. H. Hardin, Jan 26 2013

Keywords

Comments

Column 4 of A221824.

Examples

			Some solutions for n=3
..0..1..0..2....1..0..1..1....0..1..0..1....0..3..0..0....0..0..2..0
..1..4..0..0....2..3..2..0....1..2..0..4....1..1..1..2....2..0..4..0
..0..0..1..3....0..1..1..0....1..2..0..0....0..1..1..2....1..2..1..0
		

Crossrefs

Cf. A221824.
Showing 1-3 of 3 results.