login
a(n) = [ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 2 mod 3}.
0

%I #11 Jul 07 2019 02:49:50

%S 1,3,6,11,16,22,30,38,47,58,69,81,95,109,124,141,158,176,196,216,237,

%T 260,283,307,333,359,386,415,444,474,506,538,571,606,641,677,715,753,

%U 792,833,874,916,960

%N a(n) = [ (3rd elementary symmetric function of S(n))/(2nd elementary symmetric function of S(n)) ], where S(n) = {first n+2 positive integers congruent to 2 mod 3}.

%F Conjecture: a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5). G.f. x*(-1-x-x^3-x^2+x^4) / ( (1+x+x^2)*(x-1)^3 ). - _R. J. Mathar_, Oct 08 2011

%F a(n) = floor(A024392(n) / A024391(n+1)). - _Sean A. Irvine_, Jul 07 2019

%Y Cf. A024391, A024392.

%K nonn

%O 1,2

%A _Clark Kimberling_