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A378286 a(n) = number of terms in row n of the array A378282.

%I A378286 #4 Dec 21 2024 01:05:39
%S A378286 1,1,1,2,2,3,4,5,7,11,16,23,35,51,75,113,168,249,374,560,840,1262,
%T A378286 1896,2844,4270,6405,9607,14421,21633,32449,48676,73027,109546,164334,
%U A378286 246528,369784,554686,832046,1248073,1872168,2808326,4212710,6319089,9478842
%N A378286 a(n) = number of terms in row n of the array A378282.
%e A378286 First eleven rows of array A378282:
%e A378286 1
%e A378286 1
%e A378286 2
%e A378286 1  1
%e A378286 1  2
%e A378286 2  1  1
%e A378286 1  1  2  1
%e A378286 1  2  1  1  2
%e A378286 2  1  1  2  1  2  2
%e A378286 1  1  2  1  2  2  1  2  2  1  1
%e A378286 1  2  1  1  2  1  1  2  2  1  2  2  1  1  2  2  1
%e A378286 a(11) = 16 = number of terms in row 11.
%t A378286 invRE[seq_, k_] := Flatten[Map[ConstantArray[#[[2]], #[[1]]] &,
%t A378286     Partition[Riffle[seq, {k, 2 - Mod[k + 1, 2]}, {2, -1, 2}], 2]]];
%t A378286 row1 = {1}; rows = {row1};
%t A378286 col = PadRight[{}, 30, {1, 1, 2}](*112112112112112112...*);
%t A378286 Do[AppendTo[rows, invRE[Last[rows], col[[n]]]], {n, 2, Length[col]}]
%t A378286 rows // ColumnForm; (* A378282 *)
%t A378286 Map[Length, rows]  (* this sequence *)
%t A378286 (* _Peter J. C. Moses_, Nov 21 2024 *)
%Y A378286 Cf. A378282.
%K A378286 nonn
%O A378286 1,4
%A A378286 _Clark Kimberling_, Dec 20 2024