A081342 a(n) = (8^n + 2^n)/2.

1, 5, 34, 260, 2056, 16400, 131104, 1048640, 8388736, 67109120, 536871424, 4294968320, 34359740416, 274877911040, 2199023263744, 17592186060800, 140737488388096, 1125899906908160, 9007199254872064, 72057594038190080, 576460752303947776, 4611686018428436480

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).

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

a(n) = A074603(n)/2. - Michel Marcus, Jan 09 2020

Maple

seq( (8^n + 2^n)/2, n=0..30); # G. C. Greubel, Jan 08 2020

Mathematica

Table[(8^n + 2^n)/2, {n, 0, 30}] (* 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
(Sage) [(8^n + 2^n)/2 for n in (0..30)] # G. C. Greubel, Jan 08 2020
(GAP) List([0..30], n-> (8^n + 2^n)/2); # G. C. Greubel, Jan 08 2020

Crossrefs

Cf. A074603, A025551, A081343.

Sequence in context: A083987 A002776 A333804 * A248055 A365218 A243659

Adjacent sequences: A081339 A081340 A081341 * A081343 A081344 A081345

Keyword

easy,nonn

Author

Paul Barry, Mar 18 2003

Status

approved