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A081182 5th binomial transform of (0,1,0,2,0,4,0,8,0,16,...). 6
0, 1, 10, 77, 540, 3629, 23870, 155233, 1003320, 6462841, 41552050, 266875157, 1713054420, 10992415589, 70523904230, 452413483753, 2902085040240, 18615340276081, 119405446835290, 765901642003037, 4912691142818700 (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 (10,-23).

FORMULA

a(n) = 10a(n-1) - 23a(n-2), a(0)=0, a(1)=1.

G.f.: x/(1 - 10x + 23x^2).

a(n) = ((5 + sqrt(2))^n - (5 - sqrt(2))^n/(2*sqrt(2)).

a(n) = Sum_{k=0..n} C(n,2k+1) 2^k*5^(n-2k-1).

E.g.f.: exp(5*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017

MATHEMATICA

Join[{a=0, b=1}, Table[c=10*b-23*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011 *)

CoefficientList[Series[x / (1 - 10 x + 23 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)

PROG

(Sage) [lucas_number1(n, 10, 23) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 26 2009

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 10*Self(n-1)-23*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 06 2013

CROSSREFS

Binomial transform of A081181.

Cf. A081183.

Sequence in context: A159579 A244720 A081678 * A127536 A016201 A080618

Adjacent sequences:  A081179 A081180 A081181 * A081183 A081184 A081185

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 12 2003

STATUS

approved

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Last modified October 17 13:57 EDT 2019. Contains 328113 sequences. (Running on oeis4.)