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A081342 a(n) = (8^n + 2^n)/2. 11
1, 5, 34, 260, 2056, 16400, 131104, 1048640, 8388736, 67109120, 536871424, 4294968320, 34359740416, 274877911040, 2199023263744, 17592186060800, 140737488388096, 1125899906908160, 9007199254872064, 72057594038190080, 576460752303947776, 4611686018428436480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A034494. 5th binomial transform of (1,0,9,0,81,0,729,0,...).

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (10,-16).

FORMULA

a(n) = (8^n + 2^n)/2.

a(n) = 10*a(n-1) - 16*a(n-2), a(0)=1, a(1)=5.

G.f.: (1-5*x)/((1-2*x)*(1-8*x)).

E.g.f.: exp(5*x)*cosh(3*x).

((5+sqrt(9))^n + (5-sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008

MATHEMATICA

Table[(8^n + 2^n)/2, {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)

PROG

(MAGMA) [(8^n+2^n)/2: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011

(PARI) a(n)=(8^n+2^n)/2 \\ Charles R Greathouse IV, Sep 28 2015

CROSSREFS

Cf. A025551, A081343.

Sequence in context: A078284 A083987 A002776 * A248055 A243659 A058248

Adjacent sequences:  A081339 A081340 A081341 * A081343 A081344 A081345

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 18 2003

STATUS

approved

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Last modified October 21 12:36 EDT 2018. Contains 316419 sequences. (Running on oeis4.)