A081184 7th binomial transform of (0,1,0,2,0,4,0,8,0,16,...).

0, 1, 14, 149, 1428, 12989, 114730, 995737, 8548008, 72872473, 618458246, 5233409213, 44200191420, 372832446869, 3142245259426, 26468308629121, 222870793614672, 1876180605036721, 15791601170624510, 132901927952017253

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.

Index entries for linear recurrences with constant coefficients, signature (14,-47).

Formula

a(n) = 14*a(n-1) - 47*a(n-2), a(0)=0, a(1)=1.

G.f.: x/(1 - 14*x + 47*x^2). [Corrected by Georg Fischer, May 15 2019]

a(n) = ((7 + sqrt(2))^n - (7 - sqrt(2))^n)/(2*sqrt(2)).

a(n) = Sum_{k=0..n} C(n,2*k+1) * 2^k * 7^(n-2*k-1).

E.g.f.: exp(7*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017

Mathematica

CoefficientList[Series[x/(1-14*x+47*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 07 2013 *)
LinearRecurrence[{14, -47}, {0, 1}, 30] (* Harvey P. Dale, Nov 12 2013 *)

Prog

(Magma) [n le 2 select n-1 else 14*Self(n-1)-47*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 07 2013
(SageMath)
A081184=BinaryRecurrenceSequence(14, -47, 0, 1)
[A081184(n) for n in range(31)] # G. C. Greubel, Jan 14 2024

Crossrefs

Binomial transform of A081183.

Cf. A081185.

Sequence in context: A065899 A162965 A067103 * A032343 A222614 A019521

Adjacent sequences: A081181 A081182 A081183 * A081185 A081186 A081187

Keyword

nonn,easy

Author

Paul Barry, Mar 11 2003

Status

approved