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A049086
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Number of tilings of 4 X 3n rectangle by 1 X 3 rectangles. Rotations and reflections are considered distinct tilings.
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0
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1, 3, 13, 57, 249, 1087, 4745, 20713, 90417, 394691, 1722917, 7520929, 32830585, 143313055, 625594449, 2730863665, 11920848033, 52037243619, 227154537661, 991581805481, 4328482658041, 18894822411423, 82480245888473
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = 5*a(n-1) - 3*a(n-2) + a(n-3).
a(n)/a(n-1) tends to 4.3652300134...an eigenvalue of the matrix M and an inverse root of the polynomial x^3 - 3x^2 + 5x - 1. [a(n-2), a(n-1), a(n)] = M^n * [1 1 1], where M = the 3 X 3 matrix [ 5 -3 1 / 1 0 0 / 0 1 0]. E.g. a(3), a(4), a(5) = 57, 249, 1087. M^5 * [1 1 1] = [57, 249, 1087] - Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 25 2004
G.f.: (1-x)^2/(1-5*x+3*x^2-x^3). [Colin Barker, Feb 03 2012]
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MAPLE
| a[0]:=1:a[1]:=3:a[2]:=13: for n from 3 to 25 do a[n]:=5*a[n-1]-3*a[n-2]+a[n-3] od: seq(a[n], n=0..25); (Deutsch)
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CROSSREFS
| Cf. A005178, A000930.
Sequence in context: A151220 A151221 A020515 * A010921 A163606 A115968
Adjacent sequences: A049083 A049084 A049085 * A049087 A049088 A049089
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KEYWORD
| easy,nonn,changed
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AUTHOR
| Allan C. Wechsler (acw(AT)alum.mit.edu)
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EXTENSIONS
| More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 15 2005
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