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%I #22 Mar 22 2020 03:59:27
%S 1,6,24,82,261,804,2440,7356,22113,66394,199248,597822,1793557,
%T 5380776,16142448,48427480,145282593,435847950,1307544040,3922632330,
%U 11767897221,35303691916,105911076024,317733228372,953199685441
%N Partial sums of A000340, second partial sums of A003462.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
%D P. Ribenhoim, The Little Book of Big Primes, Springer-Verlag, N.Y., 1991, p. 53.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,10,-3).
%F a(n) = ((3^(n+3)) - (2*(n^2) + 12n + 19))/8.
%F a(n) = 3a(n-1)+C(n+2,2); a(0)=1.
%F a(n) = sum{k=0..n, binomial(n+3, k+3)2^k}. - _Paul Barry_, Aug 20 2004
%F From _Colin Barker_, Dec 18 2012: (Start)
%F a(n) = 6*a(n-1) - 12*a(n-2) + 10*a(n-3) - 3*a(n-4).
%F G.f.: 1/((x-1)^3*(3*x-1)). (End)
%t LinearRecurrence[{6,-12,10,-3},{1,6,24,82},40] (* _Harvey P. Dale_, Sep 05 2013 *)
%Y Cf. A003462, A000340.
%K easy,nonn
%O 0,2
%A _Barry E. Williams_, Jan 23 2000
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