A152105 a(n) = (10^n + 6^n)/2.

1, 8, 68, 608, 5648, 53888, 523328, 5139968, 50839808, 505038848, 5030233088, 50181398528, 501088391168, 5006530347008, 50039182082048, 500235092492288, 5001410554953728, 50008463329722368, 500050779978334208, 5000304679870005248, 50001828079220031488, 500010968475320188928

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (16,-60).

Crossrefs

Cf. A081186, A098158.

Programs

Mathematica

LinearRecurrence[{16,-60},{1,8},30] (* Harvey P. Dale, Jan 27 2015 *)

Formula

a(n) = (10^n + 6^n)/2. - Klaus Brockhaus, Nov 26 2008

From Philippe Deléham, Nov 26 2008: (Start)

a(n) = 16*a(n-1) - 60*a(n-2), n > 1; a(0)=1, a(1)=8.

G.f.: (1-8*x)/((1-6*x)*(1-10*x)).

a(n) = (Sum_{k=0..n} A098158(n,k)*2^(4*k))/2^n. (End)

a(n) = 2^n*A081186(n). - R. J. Mathar, Feb 04 2021

E.g.f.: exp(8*x)*cosh(2*x). - Elmo R. Oliveira, Aug 23 2024

Extensions

Extended beyond a(6) by Klaus Brockhaus, Nov 26 2008

a(19)-a(21) from Elmo R. Oliveira, Aug 23 2024