A247595 a(n) = 4*a(n-1) - 4*a(n-2) + 4*a(n-3) with a(0) = 1, a(1) = 3, a(2) = 10.

1, 3, 10, 32, 100, 312, 976, 3056, 9568, 29952, 93760, 293504, 918784, 2876160, 9003520, 28184576, 88228864, 276191232, 864587776, 2706501632, 8472420352, 26522025984, 83024429056, 259899293696, 813587562496, 2546850791424, 7972650090496, 24957547446272

Offset

0,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-4,4).

Formula

G.f.: (1 - x + 2*x^2) / (1 - 4*x + 4*x^2 - 4*x^3).

0 = a(n) - 4*a(n-1) + 4*a(n-2) - 4*a(n-3) for all n in Z.

a(n) = A061279(2*n) for all n in Z.

Binomial transform of A247594.

Example

G.f. = 1 + 3*x + 10*x^2 + 32*x^3 + 100*x^4 + 312*x^5 + 976*x^6 + 3056*x^7 + ...

Mathematica

CoefficientList[Series[(1-x+2*x^2)/(1-4*x+4*x^2-4*x^3), {x, 0, 60}], x] (* G. C. Greubel, Aug 04 2018 *)

Prog

(PARI) {a(n) = if( n<0, polcoeff( (2*x - x^2 + x^3) / (4 - 4*x + 4*x^2 - x^3) + x * O(x^-n), -n), polcoeff( (1 - x + 2*x^2) / (1 - 4*x + 4*x^2 - 4*x^3) + x * O(x^n), n))};
(Haskell)
a247595 n = a247595_list !! n
a247595_list = 1 : 3 : 10 : map (* 4) (zipWith3 (((+) .) . (-))
   (drop 2 a247595_list) (tail a247595_list) a247595_list)
-- Reinhard Zumkeller, Sep 21 2014
(Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1 - x +2*x^2)/(1-4*x+4*x^2-4*x^3)));  // G. C. Greubel, Aug 04 2018

Crossrefs

Cf. A061279, A247594.

Sequence in context: A038731 A244762 A053581 * A092822 A017935 A134377

Adjacent sequences: A247592 A247593 A247594 * A247596 A247597 A247598

Keyword

nonn

Author

Michael Somos, Sep 20 2014

Status

approved