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%I #5 Oct 13 2017 21:40:45
%S 1,1,3,6,12,21,39,66,114,192,324,531,888,1452,2382,3891,6363,10329,
%T 16833,27303,44349,71907,116625,188859,306114,495615,802632,1299255,
%U 2103504,3404259,5510376,8917248,14431590,23353131,37791414,61150962,98953434,160115403,259085673,419218803
%N a(1) = a(2) = 1; a(n) = ( Sum_{i|(n-1)} a(i) ) + Sum_{j|(n-2)} a(j).
%F a(n) ~ c*phi^n, where phi is the golden ratio (A001622) and c = 1.83226227102725... (conjecture).
%t a[n_] := a[n] = Sum[a[i], {i, Divisors[n - 1]}] + Sum[a[j], {j, Divisors[n - 2]}]; a[1] = a[2] = 1; Table[a[n], {n, 1, 40}]
%Y Cf. A000045, A001622, A003238, A007439.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Oct 13 2017
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