A152263 a(n) = ((8 + sqrt(6))^n + (8 - sqrt(6))^n)/2.

1, 8, 70, 656, 6436, 64928, 665560, 6883136, 71527696, 745221248, 7774933600, 81176105216, 847871534656, 8857730451968, 92547138221440, 967005845328896, 10104359508418816, 105583413105625088, 1103281758201710080

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

Keywords

• nonn

Comments

Binomial transform of A152262. Inverse binomial transform of A152264. - Philippe Deléham, Dec 03 2008

Links

• Index entries for linear recurrences with constant coefficients, signature (16, -58).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-6); S:=[ ((8+r6)^n+(8-r6)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008

Mathematica

LinearRecurrence[{16,-58},{1,8},20] (* Harvey P. Dale, Jul 09 2021 *)

Formula

From Philippe Deléham, Dec 03 2008: (Start)

a(n) = 16*a(n-1) - 58*a(n-2), n > 1; a(0)=1, a(1)=8.

G.f.: (1-8*x)/(1-16*x+58*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*6^(n-k). (End)

Extensions

Extended beyond a(6) by Klaus Brockhaus, Dec 03 2008