A147688 a(n) = ((6 + sqrt(8))^n + (6 - sqrt(8))^n)/2.

1, 6, 44, 360, 3088, 26976, 237248, 2091648, 18456832, 162915840, 1438198784, 12696741888, 112091336704, 989587267584, 8736489783296, 77129433907200, 680931492954112, 6011553766047744, 53072563389857792, 468547255228956672

Offset: 0

Author

Al Hakanson (hawkuu(AT)gmail.com), Nov 10 2008

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (12, -28).

Programs

Magma

Z:= PolynomialRing(Integers()); N:=NumberField(x^2-8); S:=[ ((6+r8)^n+(6-r8)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 13 2008

Mathematica

LinearRecurrence[{12,-28},{1,6},30]  (* Harvey P. Dale, Apr 23 2011 *)

Formula

From Philippe Deléham, Nov 13 2008: (Start)

a(n) = 12*a(n-1) - 28*a(n-2), a(0)=1, a(1)=6.

G.f.: (1-6x)/(1-12x+28x^2).

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

a(n) = 2^n*A083878(n). - R. J. Mathar, Feb 04 2021

Extensions

Extended beyond a(6) by Klaus Brockhaus, Nov 13 2008