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

Offset: 0

Author

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

Keywords

• nonn

Comments

Binomial transform is A152267, inverse binomial transform is A147689.

Links

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

Crossrefs

Cf. A081180, A098158, A152267, A147689.

Programs

Magma

Z:= PolynomialRing(Integers()); N:=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

Formula

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

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

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

Extensions

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

Edited by Klaus Brockhaus, Jul 09 2009