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A071954 a(n) = 4*a(n-1) - a(n-2) - 4, with a(0)=2, a(1)=4. 6
2, 4, 10, 32, 114, 420, 1562, 5824, 21730, 81092, 302634, 1129440, 4215122, 15731044, 58709050, 219105152, 817711554, 3051741060, 11389252682, 42505269664, 158631825970, 592022034212, 2209456310874, 8245803209280, 30773756526242, 114849222895684 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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).

REFERENCES

M. E. Larsen, "Four Cubes" in Puzzler's Tribute, Ed. D. Wolfe & T. Rodgers, pp. 69-70, A. K. Peters, MA, 2002

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..100

Index entries for linear recurrences with constant coefficients, signature (5,-5,1).

FORMULA

a(0)=2, a(1)=4, a(2)=10, a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3) for n > 2.

G.f.: (6*x-2)/((x-1)*(1+(x-4)*x)). - Harvey P. Dale, May 05 2011

a(n) = (2+(-(2-sqrt(3))^n+(2+sqrt(3))^n)/sqrt(3)). - Colin Barker, Nov 03 2016

A263942(n) = -a(-1-n) for all n in Z. - Michael Somos, Nov 03 2016

EXAMPLE

G.f. = 2 + 4*x + 10*x^2 + 32*x^3 + 114*x^4 + 420*x^5 + 1562*x^6 + ...

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] (* Harvey P. Dale, May 05 2011 *)

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

(PARI) {a(n) = my(w=quadgen(12)); simplify( 2 + ((2+w)^n - (2-w)^n) / w)}; /* Michael Somos, Nov 03 2016 */

CROSSREFS

Equals A052530(n) + 2, n>0. Cf. A001075, A003699.

Cf. A263942.

Sequence in context: A296003 A263662 A151400 * A120017 A000736 A263663

Adjacent sequences:  A071951 A071952 A071953 * A071955 A071956 A071957

KEYWORD

nice,nonn,easy

AUTHOR

Lekraj Beedassy, Jun 25 2002

EXTENSIONS

Edited by Robert G. Wilson v, Jun 27 2002

STATUS

approved

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Last modified February 20 04:39 EST 2018. Contains 299358 sequences. (Running on oeis4.)