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A137247
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a(n) = 4a(n-1) - 6a(n-2) + 6a(n-3) - 3a(n-4), with initial terms 0, 0, 0, 1.
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0
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0, 0, 0, 1, 4, 10, 22, 49, 112, 256, 580, 1309, 2956, 6682, 15106, 34141, 77152, 174352, 394024, 890473, 2012404, 4547866, 10277806, 23227033, 52491280, 118626160, 268085740, 605852581, 1369179004, 3094236490, 6992730202, 15803018149
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OFFSET
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0,5
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COMMENTS
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Essentially the partial sums of A052103. - R. J. Mathar, Apr 01 2008
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LINKS
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Table of n, a(n) for n=0..31.
Index entries for linear recurrences with constant coefficients, signature (4, -6, 6, -3).
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FORMULA
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From R. J. Mathar, Apr 01 2008: (Start)
O.g.f.: x^3/((x-1)*(3*x^3-3*x^2+3*x-1)).
A052103(n) = a(n+2) - a(n+1). (End)
a(n) = -1/2 + (1/6)*(1+((1/2)*i)*108^(1/6) - (1/2)*2^(1/3))^n + (1/6)*(1-(1/2)*i)*108^(1/6) - (1/2)*2^(1/3))^n + (1/6)*(1+2^(1/3))^n, with n >= 0 and i=sqrt(-1). - Paolo P. Lava, Jun 09 2008
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MAPLE
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a[0]:=0: a[1]:=0: a[2]:=0: a[3]:=1: for n from 4 to 30 do a[n]:=4*a[n-1]-6*a[n-2]+6*a[n-3]-3*a[n-4] end do: seq(a[n], n=0..30); # Emeric Deutsch, Mar 17 2008
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CROSSREFS
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Cf. A052103.
Sequence in context: A056112 A118430 A178452 * A155407 A318416 A124697
Adjacent sequences: A137244 A137245 A137246 * A137248 A137249 A137250
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz, Mar 10 2008
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EXTENSIONS
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More terms from R. J. Mathar, Rolf Pleisch and Emeric Deutsch, Apr 01 2008
Name edited by Michel Marcus, Jan 29 2019
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STATUS
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approved
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