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A081570 Fifth binomial transform of F(n+1). 6
1, 6, 37, 233, 1490, 9633, 62753, 410926, 2700349, 17786985, 117346714, 774991289, 5121849473, 33865596822, 223987930325, 1481764925737, 9803764203682, 64870223394129, 429263295428641, 2840659771285310, 18798621916707821 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A081569.

Case k=5 of family of recurrences a(n) = (2k+1)*a(n-1) - A028387(k-1)*a(n-2), a(0)=1, a(1)=k+1.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (11,-29).

FORMULA

a(n) = 11*a(n-1)-29*a(n-2), a(0)=1, a(1)=6.

a(n) = (1/2 - sqrt(5)/10)*(11/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)*(sqrt(5)/2 + 11/2)^n .

G.f.: (1-5*x)/(1-11*x+29*x^2).

a(n) = Sum_{k, 0<=k<=n} A094441(n,k)*5^k. [Philippe Deléham, Dec 14 2009]

MATHEMATICA

CoefficientList[Series[(1 - 5 x) / (1 - 11 x + 29 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 09 2013 *)

PROG

(MAGMA) I:=[1, 6]; [n le 2 select I[n] else 11*Self(n-1)-29*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 09 2013

CROSSREFS

Cf. A000045.

Sequence in context: A192807 A076026 A161734 * A122898 A218186 A317629

Adjacent sequences:  A081567 A081568 A081569 * A081571 A081572 A081573

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 22 2003

STATUS

approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)