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A295271 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 4 1s. 1
13, 98, 811, 6659, 54773, 449827, 3697742, 30386185, 249719021, 2052217315, 16865303569, 138600705864, 1139033988179, 9360690397437, 76927054505407, 632193927094967, 5195430458657358, 42696546916624813, 350884326612255131 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 4 of A295275.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Maple-assisted proof of formula

FORMULA

Empirical: a(n) = 4*a(n-1) +27*a(n-2) +63*a(n-3) +14*a(n-4) -110*a(n-5) -43*a(n-6) -45*a(n-7) +89*a(n-8) -150*a(n-9) +89*a(n-10) -126*a(n-11) +72*a(n-12) -30*a(n-13) +8*a(n-14) -2*a(n-15) +a(n-16).

From Robert Israel, Nov 19 2017: (Start)

Empirical formula confirmed (see link).

G.f.: (13*x+46*x^2+68*x^3-50*x^4-116*x^5-93*x^6+31*x^7-28*x^8-60*x^9+2*x^10-73*x^11+51*x^12-22*x^13+7*x^14-x^15+x^16)/(1-4*x-27*x^2-63*x^3-14*x^4+110*x^5+43*x^6+45*x^7-89*x^8+150*x^9-89*x^10+126*x^11-72*x^12+30*x^13-8*x^14+2*x^15-x^16).

(End)

EXAMPLE

Some solutions for n=4

..1..1..0..1....1..0..1..0....0..0..0..1....0..1..0..1....0..1..0..0

..0..0..1..0....0..0..0..1....0..0..0..0....1..0..1..0....1..0..1..0

..1..0..1..0....0..0..0..0....1..0..0..0....0..1..1..1....0..0..0..1

..0..0..0..0....0..0..0..1....0..1..0..1....1..0..1..0....0..1..0..1

MAPLE

R:= [13, 98, 811, 6659, 54773, 449827, 3697742, 30386185, 249719021, 2052217315, 16865303569, 138600705864, 1139033988179, 9360690397437, 76927054505407, 632193927094967]:

rec:= a(n) = 4*a(n-1) +27*a(n-2) +63*a(n-3) +14*a(n-4) -110*a(n-5) -43*a(n-6) -45*a(n-7) +89*a(n-8) -150*a(n-9) +89*a(n-10) -126*a(n-11) +72*a(n-12) -30*a(n-13) +8*a(n-14) -2*a(n-15) +a(n-16):

f:= gfun:-rectoproc({rec, seq(a(i)=R[i], i=1..16)}, a(n), remember):

map(f, [$1..40]); # Robert Israel, Nov 19 2017

CROSSREFS

Cf. A295275.

Sequence in context: A075899 A006976 A282992 * A034270 A201427 A155646

Adjacent sequences:  A295268 A295269 A295270 * A295272 A295273 A295274

KEYWORD

nonn

AUTHOR

R. H. Hardin, Nov 19 2017

STATUS

approved

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Last modified September 22 03:20 EDT 2021. Contains 347605 sequences. (Running on oeis4.)