A145303 a(n) = ((8 + sqrt(8))^n + (8 - sqrt(8))^n)/2.

1, 8, 72, 704, 7232, 76288, 815616, 8777728, 94769152, 1024753664, 11088986112, 120037572608, 1299617939456, 14071782965248, 152369922834432, 1649898919297024, 17865667030024192, 193456332999753728, 2094823974314704896, 22683628941049069568, 245627920495161638912

Offset

0,2

Comments

Binomial transform is A152267, inverse binomial transform is A147689.

Links

Paolo Xausa, Table of n, a(n) for n = 0..966

Index entries for linear recurrences with constant coefficients, signature (16,-56).

Formula

From R. J. Mathar, Oct 10 2008: (Start)

a(n) = 16*a(n-1) - 56*a(n-2).

G.f.: (1-8*x)/(1-16*x+56*x^2).

a(n) = 2^n*A081180(n+1) - 2^(n+2)*A081180(n). (End)

a(n) = Sum_{k=0..n} 8^k*A098158(n,k). - Philippe Deléham, Oct 14 2008

Mathematica

LinearRecurrence[{16, -56}, {1, 8}, 25] (* Paolo Xausa, May 16 2026 *)

Prog

(Magma) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((8+r8)^n+(8-r8)^n)/2: n in [0..17] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Oct 20 2008
(PARI) a(n)=([0, 1; -56, 16]^n*[1; 8])[1, 1] \\ Charles R Greathouse IV, May 15 2026

Crossrefs

Cf. A081180, A098158, A152267, A147689.

Sequence in context: A078995 A264913 A082414 * A098411 A220741 A165323

Adjacent sequences: A145300 A145301 A145302 * A145304 A145305 A145306

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Oct 06 2008

Extensions

More terms from R. J. Mathar, Oct 10 2008

Edited by Klaus Brockhaus, Jul 09 2009

More terms from Paolo Xausa, May 16 2026

Status

approved