A081680 - OEIS

%I #23 Nov 10 2024 15:52:37

%S 1,2,4,23,274,2927,27094,228923,1827634,14069687,105715534,781107923,

%T 5702856394,41273440847,296753044774,2122921300523,15127554995554,

%U 107462125890407,761485887090814,5385095865086723,38019827430709114,268063860039802367,1887898846143949654,13283513097950386523

%N a(n) = (7^n - 6^n - 5^n - 4^n + 4*3^n)/2.

%C Binomial transform of A081679.

%H Harvey P. Dale, <a href="/A081680/b081680.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (25,-245,1175,-2754,2520).

%F G.f.: -(1083*x^4-762*x^3+199*x^2-23*x+1)/((3*x-1)*(4*x-1)*(5*x-1)*(6*x-1)*(7*x-1)). [_Colin Barker_, Sep 07 2012]

%F From _Elmo R. Oliveira_, Sep 13 2024: (Start)

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

%F a(n) = 25*a(n-1) - 245*a(n-2) + 1175*a(n-3) - 2754*a(n-4) + 2520*a(n-5) for n > 4. (End)

%t LinearRecurrence[{25,-245,1175,-2754,2520},{1,2,4,23,274},30] (* _Harvey P. Dale_, Feb 19 2018 *)

%Y Cf. A081679, A081681.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Mar 30 2003

%E a(21)-a(23) from _Elmo R. Oliveira_, Sep 13 2024