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%I #8 Jun 13 2015 00:53:36
%S 0,1,5,14,46,111,303,688,1712,3761,8881,19122,43698,92851,207539,
%T 436916,961204,2009781,4369077,9087670,19573430,40544951,86682295,
%U 178956984,380283576,782936761,1655351993,3400182458,7158278842
%N Partial sums of A005985.
%C Partial sums of length of longest walk on edges of n-cube. The subsequence of primes in this partial sum begins: 5, 3761, 40544951.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,3,-15,6,12,-8).
%F a(n) = SUM[i=0..n] A005985(i).
%F Empirical G.f.: x*(1+2*x-4*x^2+4*x^3)/((1-x)^2*(1+x)*(1-2*x)^2*(1+2*x)). [Colin Barker, Jan 14 2012]
%F a(0)=0, a(1)=1, a(2)=5, a(3)=14, a(4)=46, a(5)=111, a(n)=3*a(n-1)+ 3*a(n-2)- 15*a(n-3)+ 6*a(n-4)+12*a(n-5)-8*a(n-6). - _Harvey P. Dale_, Jun 11 2015
%e a(21) = 0 + 1 + 4 + 9 + 32 + 65 + 192 + 385 + 1024 + 2049 + 5120 + 10241 + 24576 + 49153 + 114688 + 229377 + 524288 + 1048577 + 2359296 + 4718593 + 10485760 + 20971521 = 40544951 is prime.
%t Accumulate[LinearRecurrence[{2,5,-10,-4,8},{0,1,4,9,32},40]] (* or *) LinearRecurrence[{3,3,-15,6,12,-8},{0,1,5,14,46,111},40] (* _Harvey P. Dale_, Jun 11 2015 *)
%Y Cf. A005985.
%K nonn
%O 0,3
%A _Jonathan Vos Post_, Apr 22 2010
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