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Search: id:A136252
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| A136252 |
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a(n)=a(n-1)+2a(n-2)-2a(n-3). |
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+0
3
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| 1, 3, 5, 9, 13, 21, 29, 45, 61, 93, 125, 189, 253, 381, 509, 765, 1021, 1533, 2045, 3069, 4093, 6141, 8189, 12285, 16381, 24573, 32765, 49149, 65533, 98301, 131069, 196605, 262141, 393213, 524285, 786429, 1048573, 1572861, 2097149, 3145725, 4194301
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A060482 without the term 2.
For n>=2, number of nXn arrays with values that are squares of integers, having all 2X2 subblocks summing to 4. [From Ron Hardin (rhhardin(AT)att.net), Apr 03 2009]
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FORMULA
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a(n)=2^((1/2)*n-1)*(4 + 4(-1)^n + 3sqrt(2)*[1-(-1)^n)]-3. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2008
a(n) = -2*(1 + sqrt(2))^(-1)*a(0)*(1-sqrt(2))^(-1)-1/4*sqrt(2)*sqrt(2)^n*(1-sqrt(2))^(-1) *a(2) + 1/2*sqrt(2)^n*a(0)*(1-sqrt(2))^(-1) + (-4-2*sqrt(2))^(-1)*(-sqrt(2))^n*a(1) + (-4-2*sqrt(2))^(-1)*sqrt(2)*(-sqrt(2))^n*a(1)-(-4-2*sqrt(2))^(-1)*sqrt(2)*( -sqrt(2))^n*a(0)-1/2*sqrt(2)^n*a(1)*(1-sqrt(2))^(-1) + (1 + sqrt(2))^(-1)*(1 -sqrt(2))^(-1)*a(2)-(-4-2*sqrt(2))^(-1)*(-sqrt(2))^n*a(2) + 1/4*sqrt(2)*sqrt(2)^n *a(1)*(1-sqrt(2))^(-1) - Alexander R. Povolotsky (pevnev(AT)juno.com), Mar 31 2008
G.f.: (1+2*x)/((1-x)*(1-2*x^2)) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Aug 30 2009]
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MAPLE
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a:=proc(n) options operator, arrow: 2^((1/2)*n-1)*(4+4*(-1)^n+3*sqrt(2)*(1-(-1)^n))-3 end proc: seq(a(n), n=0..40); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2008
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CROSSREFS
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Same recurrence as in A135530.
Sequence in context: A076274 A058989 A049691 this_sequence A141325 A146905 A052282
Adjacent sequences: A136249 A136250 A136251 this_sequence A136253 A136254 A136255
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Mar 17 2008
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Apr 18 2008
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 31 2008
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