A155132 a(n) = 8*a(n-1) + 8*a(n-2), n > 2, a(0)=1, a(1)=7, a(2)=63.

1, 7, 63, 560, 4984, 44352, 394688, 3512320, 31256064, 278147072, 2475225088, 22026977280, 196017618944, 1744356769792, 15522995109888, 138138815037440, 1229294481178624, 10939466369728512, 97350086807257088

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (8,8).

Formula

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

a(n) = (1/8)*[n=0] - 7*(2*sqrt(2)*i)^(n-2)*ChebyshevU(n, -sqrt(2)*I). - G. C. Greubel, Mar 24 2021

Mathematica

With[{m=8}, LinearRecurrence[{m, m}, {1, m-1, m^2-1}, 30]] (* G. C. Greubel, Mar 24 2021 *)
LinearRecurrence[{8, 8}, {1, 7, 63}, 20] (* Harvey P. Dale, Feb 07 2026 *)

Prog

(Magma) [1] cat [n le 2 select 7*(8*n-7) else 8*(Self(n-1) + Self(n-2)): n in [1..30]]; // G. C. Greubel, Mar 24 2021
(SageMath) [1]+[-7*(2*sqrt(2)*i)^(n-2)*chebyshev_U(n, -sqrt(2)*i) for n in (1..30)] # G. C. Greubel, Mar 24 2021
(PARI) a(n)=if(n, ([0, 1; 8, 8]^(n-1)*[7; 63])[1, 1], 1) \\ Charles R Greathouse IV, May 11 2026

Crossrefs

Sequences of the form a(n) = m*(a(n-1) + a(n-2)) with a(0)=1, a(1) = m-1, a(2) = m^2 -1: A155020 (m=2), A155116 (m=3), A155117 (m=4), A155119 (m=5), A155127 (m=6), A155130 (m=7), this sequence (m=8), A155144 (m=9), A155157 (m=10).

Sequence in context: A218237 A024088 A291034 * A270472 A266426 A368164

Adjacent sequences: A155129 A155130 A155131 * A155133 A155134 A155135

Keyword

nonn,easy

Author

Philippe Deléham, Jan 20 2009

Status

approved