login
a(n) = 8^n - 7^n - 6^n - 5^n + 3*4^n.
2

%I #26 Sep 12 2024 19:58:39

%S 1,2,2,20,542,8132,94502,964700,9138782,82619732,724180502,6213565580,

%T 52507598222,438786732932,3636161064902,29939329241660,

%U 245281233244862,2001531240407732,16280816416067702,132088684297864940,1069381010972414702,8642425579112444132,69743202133180068902

%N a(n) = 8^n - 7^n - 6^n - 5^n + 3*4^n.

%C Binomial transform of A081686.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (30,-355,2070,-5944,6720).

%F G.f.: -(2456*x^4-1400*x^3+297*x^2-28*x+1)/((4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)). - _Colin Barker_, Aug 12 2012

%F From _Elmo R. Oliveira_, Sep 12 2024: (Start)

%F E.g.f.: exp(4*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).

%F a(n) = 30*a(n-1) - 355*a(n-2) + 2070*a(n-3) - 5944*a(n-4) + 6720*a(n-5) for n > 4. (End)

%Y Cf. A081686, A081890.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 30 2003

%E a(20)-a(22) from _Elmo R. Oliveira_, Sep 12 2024