A102303 - OEIS

%I #19 Feb 04 2024 03:22:30

%S 1,9,57,401,2801,19609,137257,960801,6725601,47079209,329554457,

%T 2306881201,16148168401,113037178809,791260251657,5538821761601,

%U 38771752331201,271402266318409,1899815864228857,13298711049602001,93090977347214001,651636841430498009

%N a(n) = (1/6) * (7^(n+1) - 3*(-1)^n + 2).

%H G. C. Greubel, <a href="/A102303/b102303.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,1,-7).

%F From _Chai Wah Wu_, Mar 11 2021: (Start)

%F a(n) = 7*a(n-1) + a(n-2) - 7*a(n-3) for n > 2.

%F G.f.: -(1 + 2*x - 7*x^2)/((1 - x)*(1 + x)*(1 - 7*x)). (End)

%F From _G. C. Greubel_, Feb 03 2024: (Start)

%F a(n) = A023000(n+1) + A000035(n).

%F E.g.f.: (1/6)*(-3*exp(-x) + 2*exp(x) + 7*exp(7*x)). (End)

%t Table[(7^(n+1) -3*(-1)^n +2)/6, {n, 0, 50}]

%o (Magma) [(7^(n+1)-3*(-1)^n+2)/6: n in [0..50]]; // _G. C. Greubel_, Feb 03 2024

%o (SageMath) [(7^(n+1)-3*(-1)^n+2)/6 for n in range(51)] # _G. C. Greubel_, Feb 03 2024

%Y Cf. A000035, A023000.

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Mar 15 2005

%E Edited by _N. J. A. Sloane_, May 29 2007