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A206438 Triangle read by rows which lists the squares of the parts of A135010.

%I A206438 #27 May 29 2020 02:21:23
%S A206438 1,1,4,1,1,9,1,1,1,4,4,16,1,1,1,1,1,4,9,25,1,1,1,1,1,1,1,4,4,4,4,16,9,
%T A206438 9,36,1,1,1,1,1,1,1,1,1,1,1,4,4,9,4,25,9,16,49,1,1,1,1,1,1,1,1,1,1,1,
%U A206438 1,1,1,1,4,4,4,4,4,4,16,4,9,9,4,36,9,25
%N A206438 Triangle read by rows which lists the squares of the parts of A135010.
%C A206438 Volumes of the parts in the section model of partitions version "boxes" in which each part of size k has a volume = k^2. Row sums of this triangle give A206440 and partial sums of A206440 give A066183.
%H A206438 Alois P. Heinz, <a href="/A206438/b206438.txt">Rows n = 1..23, flattened</a>
%F A206438 a(n) = A135010(n)^2.
%e A206438 Written as a triangle:
%e A206438 1;
%e A206438 1,4;
%e A206438 1,1,9;
%e A206438 1,1,1,4,4,16;
%e A206438 1,1,1,1,1,4,9,25;
%e A206438 1,1,1,1,1,1,1,4,4,4,4,16,9,9,36;
%e A206438 1,1,1,1,1,1,1,1,1,1,1,4,4,9,4,25,9,16,49;
%t A206438 Table[Reverse@ConstantArray[{1}, PartitionsP[n - 1]] ~Join~ DeleteCases[Sort@PadRight[Reverse/@Cases[IntegerPartitions[n], x_ /; Last[x] != 1]], x_ /; x == 0, 2], {n, 1, 8}] ^2  // Flatten (* _Robert Price_, May 28 2020 *)
%Y A206438 Row n has length A138137(n).
%Y A206438 Row sums give A206440.
%Y A206438 Right border gives positives A000290.
%Y A206438 Cf. A066183, A135010, A138121, A141285.
%K A206438 nonn,tabf
%O A206438 1,3
%A A206438 _Omar E. Pol_, Feb 08 2012