A152429 a(n) = (11^n + 5^n)/2.

1, 8, 73, 728, 7633, 82088, 893593, 9782648, 107374753, 1179950408, 12973595113, 142680249368, 1569336258673, 17261966423528, 189877968549433, 2088639343496888, 22974941225731393, 252723895719373448

Offset: 0

Author

Philippe Deléham, Dec 03 2008

Keywords

• nonn
• less

Comments

Binomial transform of A081343.

Inverse binomial transform of A143079.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (16,-55).

Crossrefs

Cf. A162516.

Programs

GAP

List([0..20], n-> (11^n+5^n)/2); # G. C. Greubel, Jan 08 2020

Magma

[(11^n+5^n)/2: n in [0..20]]; // Vincenzo Librandi, Jun 01 2011

Maple

seq( (11^n+5^n)/2, n=0..20); # G. C. Greubel, Jan 08 2020

Mathematica

LinearRecurrence[{16,-55}, {1,8}, 20] (* G. C. Greubel, Jan 08 2020 *)

PARI

vector(21, n, (11^(n-1) + 5^(n-1))/2 ) \\ G. C. Greubel, Jan 08 2020

Sage

[(11^n+5^n)/2 for n in (0..20)] # G. C. Greubel, Jan 08 2020

Formula

a(n) = 16*a(n-1) - 55*a(n-2), with a(0)=1, a(1)=8.

G.f.: (1-8*x)/(1 - 16*x + 55*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*9^(n-k).

a(n) = ((8 + sqrt(9))^n + (8 - sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008

E.g.f.: (exp(11*x) + exp(5*x))/2. - G. C. Greubel, Jan 08 2020