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A059020
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Number of 2 X n checkerboards in which the set of red squares is edge connected.
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3
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0, 3, 13, 40, 108, 275, 681, 1664, 4040, 9779, 23637, 57096, 137876, 332899, 803729, 1940416, 4684624, 11309731, 27304157, 65918120, 159140476, 384199155, 927538873, 2239276992, 5406092952, 13051462995, 31509019045, 76069501192
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=2a(n-1)+a(n-2)+4n-1
a(n)=-7/2+(7/4)*[1+sqrt(2)]^n-2*n-(5/4)*sqrt(2)*[1-sqrt(2)]^n+(7/4)*[1-sqrt(2)]^n+(5/4)*[1 +sqrt(2)]^n*sqrt(2), with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 10 2008
a(n)=3a(n-1)-a(n-2)-a(n-3)+4; a(n)=4a(n-1)-4a(n-2)+a(n-4); [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Nov 23 2008]
G.f.: x*(3+x)/((1-2*x-x^2)*(1-x)^2) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 28 2009]
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CROSSREFS
| Empirical observations (from Superseeker): (1) if b(n)=a(n)+n then {b(n)} is A048777, (2) if b(n)=a(n+3)-3a(n+2)-3a(n+1)+a(n) then {b(n)} is A052542 and (3) if b(n)=a(n+2)-2(a(n+1)+a(n) then {b(n)} is A001333.
See also A059021.
Cf. A000129. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Sep 28 2009]
Sequence in context: A167910 A147042 A018492 * A095109 A049167 A173867
Adjacent sequences: A059017 A059018 A059019 * A059021 A059022 A059023
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Dec 14 2000
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