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A071954
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a(n) = 4*a(n-1) - a(n-2) - 4, with a(0)=2, a(1)=4.
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5
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2, 4, 10, 32, 114, 420, 1562, 5824, 21730, 81092, 302634, 1129440, 4215122, 15731044, 58709050, 219105152, 817711554, 3051741060, 11389252682, 42505269664, 158631825970, 592022034212, 2209456310874, 8245803209280
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n) gives the side of a cube having a square number of cubes in its two outermost layers, i.e. solutions p to the equation p^3 - (p-4)^3 = q^2. The corresponding q is given by 4*A001075(n).
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REFERENCES
| M. E. Larsen, "Four Cubes" in Puzzler's Tribute, Ed. D. Wolfe & T. Rodgers, pp. 69-70, A. K. Peters, MA, 2002
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..100
Index to sequences with linear recurrences with constant coefficients, signature (5,-5,1).
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FORMULA
| a(0)=2, a(1)=4, a(2)=10, a(n)=5a(n-1)-5a(n-2)+a(n-3)
G.f.: (6x-2)/((x-1) (1+(x-4)x)) [From Harvey P. Dale, May 05 2011]
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MATHEMATICA
| a[n_] := a[n] = 4*a[n - 1] - a[n - 2] - 4; a[0] = 2; a[1] = 4; Table[ a[n], {n, 0, 25}]
LinearRecurrence[{5, -5, 1}, {2, 4, 10}, 40] (* From Harvey P. Dale, May 05 2011 *)
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PROG
| (Haskell)
a071954 n = a071954_list !! n
a071954_list = 2 : 4 : zipWith (-)
(map ((4 *) . pred) (tail a071954_list)) a071954_list
-- Reinhard Zumkeller, Aug 11 2011
(PARI) Vec((2-6*x)/(1-5*x+5*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Feb 09 2012
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CROSSREFS
| Equals A052530(n) + 2, n>0. Cf. A003699.
Sequence in context: A005269 A070900 A151400 * A120017 A000736 A176006
Adjacent sequences: A071951 A071952 A071953 * A071955 A071956 A071957
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KEYWORD
| nice,nonn,easy,changed
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 25 2002
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 27 2002
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