VOOZH about

URL: https://oeis.org/A247595

⇱ A247595 - OEIS

login
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
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
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 *)
LinearRecurrence[{4, -4, 4}, {1, 3, 10}, 30] (* Harvey P. Dale, Jan 05 2026 *)
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
Sequence in context: A038731 A244762 A053581 * A092822 A017935 A134377
KEYWORD
nonn
AUTHOR
Michael Somos, Sep 20 2014
STATUS
approved