A081343 a(n) = (10^n + 4^n)/2.

1, 7, 58, 532, 5128, 50512, 502048, 5008192, 50032768, 500131072, 5000524288, 50002097152, 500008388608, 5000033554432, 50000134217728, 500000536870912, 5000002147483648, 50000008589934592, 500000034359738368

Offset

0,2

Comments

Binomial transform of A025551. 7th 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 (14,-40).

Formula

a(n) = 14*a(n-1) -40*a(n-2), a(0)=1, a(1)=7.

G.f.: (1-7*x)/((1-4*x)*(1-10*x)).

E.g.f.: exp(7*x) * cosh(3*x).

a(n) = ((7+sqrt(9))^n + (7-sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008

Maple

seq( (10^n + 4^n)/2, n=0..25); # G. C. Greubel, Jan 07 2020

Mathematica

CoefficientList[Series[(1-7x)/((1-4x)(1-10x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 08 2013 *)

Prog

(Magma) [(10^n+4^n)/2: n in [0..25]]; // Vincenzo Librandi, Aug 08 2013
(PARI) a(n)=(10^n+4^n)/2 \\ Charles R Greathouse IV, Oct 07 2015
(Sage) [(10^n + 4^n)/2 for n in (0..25)] # G. C. Greubel, Jan 07 2020
(GAP) List([0..25], n-> (10^n + 4^n)/2); # G. C. Greubel, Jan 07 2020

Crossrefs

Cf. A081342.

Sequence in context: A139397 A194724 A308650 * A163048 A318233 A367321

Adjacent sequences: A081340 A081341 A081342 * A081344 A081345 A081346

Keyword

easy,nonn

Author

Paul Barry, Mar 18 2003

Status

approved