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A226351 Number of ways to tile a fixed 3 X n square grid with 1 X 1, 2 X 2, and 1 X 2 tiles. 1
1, 3, 26, 163, 1125, 7546, 51055, 344525, 2326760, 15709977, 106079739, 716273960, 4836475953, 32657123299, 220509407586, 1488936665619, 10053686907525, 67885102598386, 458377829683919, 3095086053853821, 20898824215523616 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Woods, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (4,19,1,-26,1,6).

FORMULA

Recurrence: a(n) = 4*a(n-1)+19*a(n-2)+a(n-3)-26*a(n-4)+a(n-5)+6*a(n-6) for n>5, a(0)=1, a(1)=3, a(2)=26, a(3)=163, a(4)=1125, a(5)=7546.

G.f.: (1-x-5*x^2+x^3+2*x^4)/(1-4*x-19*x^2-x^3+26*x^4-x^5-6*x^6).

MATHEMATICA

LinearRecurrence[{4, 19, 1, -26, 1, 6}, {1, 3, 26, 163, 1125, 7546}, 21] (* T. D. Noe, Jun 04 2013 *)

PROG

(Python)

# Depth-first search on 3 rows and n columns

# Produces "count" and the list "result[]"

# Omit the 2nd-last line if memory runs low

n=5; rows=3

count=0; result=[]

def f(b, row=0, col=-1):

..global count

..for i in range(row, len(b)):

....for j in range((col+1 if i==row else 0), len(b[0])):

......if b[i][j]==' ':

........if i<len(b)-1:

..........if b[i+1][j]==' ':

............f(b[:i]+[b[i][:j]+'^'+b[i][j+1:], b[i+1][:j]+'V'+b[i+1][j+1:]]+b[i+2:], i, j)

............if j<len(b[0])-1:

..............if b[i][j+1]==' ' and b[i+1][j:j+2]==' ':

................f(b[:i]+[b[i][:j]+'/\\'+b[i][j+2:], b[i+1][:j]+'\\/'+b[i+1][j+2:]]+b[i+2:], i, j)

........if j<len(b[0])-1:

..........if b[i][j+1]==' ':

............f(b[:i]+[b[i][:j]+'<>'+b[i][j+2:]]+b[i+1:], i, j)

..count+=1

..result.append(b) # omit this line

f([' '*n]*rows); print(count)

CROSSREFS

Cf. A226348.

Sequence in context: A252872 A121626 A038697 * A091262 A121121 A228116

Adjacent sequences:  A226348 A226349 A226350 * A226352 A226353 A226354

KEYWORD

nonn,easy

AUTHOR

Andrew Woods, Jun 04 2013

STATUS

approved

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Last modified June 25 12:01 EDT 2019. Contains 324352 sequences. (Running on oeis4.)