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A081571 Sixth binomial transform of F(n+1). 3
1, 7, 50, 363, 2669, 19814, 148153, 1113615, 8402722, 63577171, 481991621, 3659227062, 27808295345, 211479529943, 1609093780114, 12247558413819, 93245414394973, 710040492168070, 5407464407991017, 41185377124992351 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A081570.

Case k=6 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 (13,-41).

FORMULA

a(n) = 13*a(n-1)-41*a(n-2), a(0)=1, a(1)=7.

a(n) = (1/2 - sqrt(5)/10)*(13/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)*(sqrt(5)/2 + 13/2)^n.

G.f.: (1-6*x)/(1-13*x+41*x^2).

a(n) = Sum_{k, 0<=k<=n} A094441(n,k)*6^k. [Philippe Deléham, Dec 14 2009]

MATHEMATICA

CoefficientList[Series[(1 - 6 x) / (1 - 13 x + 41 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 09 2013 *)

PROG

(MAGMA) I:=[1, 7]; [n le 2 select I[n] else 13*Self(n-1)-41*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Aug 09 2013

CROSSREFS

Cf. A000045.

Sequence in context: A022037 A054413 A163458 * A275827 A081189 A108869

Adjacent sequences:  A081568 A081569 A081570 * A081572 A081573 A081574

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 22 2003

STATUS

approved

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Last modified March 26 01:08 EDT 2019. Contains 321479 sequences. (Running on oeis4.)