%I #9 Aug 01 2015 08:52:26
%S 1,5,15,36,70,123,197,298,428,593,795,1040,1330,1671,2065,2518,3032,
%T 3613,4263,4988,5790,6675,7645,8706,9860,11113,12467,13928,15498,
%U 17183,18985,20910,22960,25141,27455,29908,32502,35243,38133,41178,44380
%N Partial sums of A049486.
%C Partial sums of maximum length of non-crossing path on n X n square lattice. The subsequence of primes in this partial sum begins: 5, 197, 593, 3613, 11113, 17183.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3, -2, -2, 3, -1).
%F a(n) = SUM[i=1..n] A049486(i).
%F Conjecture: a(n) = (3*(-9+(-1)^n)+34*n-12*n^2+8*n^3)/12 for n>1. G.f.: x*(x^5-x^4+3*x^3+2*x^2+2*x+1) / ((x-1)^4*(x+1)). - _Colin Barker_, May 02 2013
%e a(7) = 1 + 4 + 10 + 21 + 34 + 53 + 74 = 197 is prime.
%t Accumulate[Join[{1,4},LinearRecurrence[{2,0,-2,1},{10,21,34,53},40]]] (* or *) Join[{1,5},LinearRecurrence[{3,-2,-2,3,-1},{15,36,70,123,197},40]] (* _Harvey P. Dale_, Aug 21 2013 *)
%Y Cf. A049486, A049487.
%K nonn
%O 1,2
%A _Jonathan Vos Post_, Mar 25 2010
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