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A081185 8th binomial transform of (0,1,0,2,0,4,0,8,0,16,...). 7
0, 1, 16, 194, 2112, 21764, 217280, 2127112, 20562432, 197117968, 1879016704, 17842953248, 168988216320, 1597548359744, 15083504344064, 142288071200896, 1341431869882368, 12641049503662336, 119088016125890560 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (16,-62).

FORMULA

a(n) = 16*a(n-1) - 62*a(n-2), a(0)=0, a(1)=1.

G.f.: x/(1 - 16*x + 62*x^2).

a(n) = ((8 + sqrt(2))^n - (8 - 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(8*x)*sinh(sqrt(2)*x)/sqrt(2). - Ilya Gutkovskiy, Aug 12 2017

MATHEMATICA

Join[{a=0, b=1}, Table[c=16*b-62*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)

CoefficientList[Series[x / (1 - 16 x + 62 x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 07 2013 *)

LinearRecurrence[{16, -62}, {0, 1}, 30] (* Harvey P. Dale, Sep 24 2013 *)

PROG

(MAGMA) [n le 2 select n-1 else 16*Self(n-1)-62*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 07 2013

CROSSREFS

Binomial transform of A081184.

Sequence in context: A081202 A196803 A292785 * A159517 A153599 A016280

Adjacent sequences:  A081182 A081183 A081184 * A081186 A081187 A081188

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Mar 11 2003

STATUS

approved

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Last modified September 19 23:59 EDT 2019. Contains 327207 sequences. (Running on oeis4.)