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%I #16 Jun 11 2021 20:50:49
%S 1,1,2,3,5,8,15,26,48,79,137,223,403,689,1251,2088,3647,6028,10775,
%T 18386,33010,55460,96916,161705,287199,490430,873964,1475256,2575673,
%U 4325448,7646036,13072664,23169478,39254755,68456542
%N a(n) = Sum_{k=0..floor(n/2)} T(n-k, k), T given by A026692.
%H Vincenzo Librandi, <a href="/A026702/b026702.txt">Table of n, a(n) for n = 0..1000</a>
%t T[_, 0] = 1; T[n_, n_] = 1; T[n_, k_] /; EvenQ[k] && 1 <= k/2 <= Floor[n/4] || EvenQ[n - k] && 1 <= (n - k)/2 <= Floor[n/4] := T[n, k] = T[n - 1, k - 1] + T[n - 2, k - 1] + T[n - 1, k]; T[n_, k_] := T[n, k] = T[n - 1, k - 1] + T[n - 1, k];
%t a[n_] := Sum[T[n - k, k], {k, 0, Floor[n/2]}];
%t Table[a[n], {n, 0, 34}] (* _Jean-François Alcover_, Jul 02 2017 *)
%K nonn
%O 0,3
%A _Clark Kimberling_
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