A155130 a(n) = 7*a(n-1) + 7*a(n-2), n>2, a(0)=1, a(1)=6, a(2)=48.

1, 6, 48, 378, 2982, 23520, 185514, 1463238, 11541264, 91031514, 718009446, 5663286720, 44669073162, 352326519174, 2778969146352, 21919069658682, 172886271635238, 1363637389057440, 10755665624848746, 84835121097343302

Offset: 0

Author

Philippe Deléham, Jan 20 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,7).

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), this sequence (m=7), A155132 (m=8), A155144 (m=9), A155157 (m=10).

Programs

Magma

m:=7; [1] cat [n le 2 select (m-1)*(m*n-(m-1)) else m*(Self(n-1) + Self(n-2)): n in [1..30]]; // G. C. Greubel, Mar 25 2021

Maple

m:= 7; 1,seq(simplify((1-m)*(sqrt(m)*I)^(n-2)*ChebyshevU(n, -I*sqrt(m)/2)), n = 1..30); # G. C. Greubel, Mar 25 2021

Mathematica

LinearRecurrence[{7,7},{1,6,48},30] (* Harvey P. Dale, Mar 11 2018 *)

Sage

m=7; [1]+[-(m-1)*(sqrt(m)*i)^(n-2)*chebyshev_U(n, -sqrt(m)*i/2) for n in (1..30)] # G. C. Greubel, Mar 25 2021

Formula

G.f.: (1-x-x^2)/(1-7*x-7*x^2) .

a(n) = (1/7)*[n=0] - 6*(sqrt(7)*i)^(n-2)*ChebyshevU(n, -sqrt(7)*i/2). - G. C. Greubel, Mar 25 2021