A163165 a(n) = 20*a(n-1) - 96*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

1, 10, 104, 1120, 12416, 140800, 1624064, 18964480, 223379456, 2646999040, 31495553024, 375799152640, 4492409962496, 53771480596480, 644158255529984, 7721102973337600, 92582866935873536, 1110431453277061120, 13320673839697362944, 159812057279349391360

Offset: 0

Author

Klaus Brockhaus, Jul 22 2009

Keywords

• nonn
• easy

Comments

Binomial transform of A152106. Tenth binomial transform of powers of 4 interleaved with zeros.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (20,-96).

Crossrefs

Cf. A000302 (powers of 4), A152106.

Programs

Magma

[ n le 2 select 9*n-8 else 20*Self(n-1)-96*Self(n-2): n in [1..18] ];

PARI

a(n) = (12^n+8^n)/2; \\ Jinyuan Wang, Mar 23 2020

Formula

a(n) = (12^n + 8^n)/2.

G.f.: (1-10*x)/((1-8*x)*(1-12*x)).

E.g.f.: exp(10*x)*cosh(2*x). - Elmo R. Oliveira, Aug 23 2024