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A081180 4th binomial transform of (0,1,0,2,0,4,0,8,0,16,...). 9
0, 1, 8, 50, 288, 1604, 8800, 47944, 260352, 1411600, 7647872, 41420576, 224294400, 1214467136, 6575615488, 35602384000, 192760455168, 1043650265344, 5650555750400, 30593342288384, 165638957801472, 896804870374400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

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 (8,-14).

FORMULA

a(n) = 8a(n-1) - 14a(n-2), a(0)=0, a(1)=1.

G.f.: x/(1 - 8x + 14x^2).

a(n) = ((4 + sqrt(2))^n - (4 - sqrt(2))^n/(2*sqrt(2)).

a(n) = Sum_{k=0..n} C(n,2k+1) 2^k*4^(n-2k-1).

If shifted once left, fourth binomial transform of A143095. - Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009, R. J. Mathar, Oct 15 2009

E.g.f.: exp(4*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017

MATHEMATICA

Join[{a=0, b=1}, Table[c=8*b-14*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 19 2011 *)

CoefficientList[Series[x / (1 - 8 x + 14 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

LinearRecurrence[{8, -14}, {0, 1}, 30] (* Harvey P. Dale, Aug 17 2019 *)

PROG

(Sage) [lucas_number1(n, 8, 14) for n in xrange(0, 22)] # Zerinvary Lajos, Apr 23 2009

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 8*Self(n-1)-14*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 06 2013

CROSSREFS

Binomial transform of A081179.

Cf. A081182.

Sequence in context: A133357 A081675 A283277 * A052177 A127745 A243876

Adjacent sequences:  A081177 A081178 A081179 * A081181 A081182 A081183

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 11 2003

EXTENSIONS

Modified the completing comment on the fourth binomial transform - R. J. Mathar, Oct 15 2009

STATUS

approved

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Last modified September 17 12:56 EDT 2019. Contains 327131 sequences. (Running on oeis4.)