A370178 a(n) = floor(x*a(n-1)) for n > 0 where x = 4 + 2*sqrt(6), a(0) = 1.

1, 8, 71, 631, 5615, 49967, 444655, 3956975, 35213039, 313360111, 2788585199, 24815562479, 220833181423, 1965189951215, 17488185061103, 155627000098543, 1384921481277167, 12324387851005679, 109674474658262767, 975990900074147567, 8685322997859282671

Offset: 0

Author

Philippe Deléham, Apr 02 2024

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (9,0,-8).

Crossrefs

Cf. A057091, A090654 (x value), A370174.

Programs

Mathematica

LinearRecurrence[{9,0,-8},{1,8,71},21] (* James C. McMahon, Apr 21 2024 *)

Formula

a(n) = 9*a(n-1) - 8*a(n-3) for n>2, a(0) = 1, a(1) = 8, a(2) = 71.

a(n) = 8*a(n-1) + 8*a(n-2) - 1.

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

a(n) = Sum_{k=0..n} A370174(n,k)*7^k.

a(n) = (7*(8-3*sqrt(6))*(4-2*sqrt(6))^n + 7*(8+3*sqrt(6))*(4+2*sqrt(6))^n + 8)/120.

a(n) = (14*A057091(n) + 7*A057091(n-1) + 1)/15.