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A321202 Row sums of the irregular triangle A321201.

%I A321202 #17 Mar 13 2025 11:04:08
%S A321202 1,1,2,2,5,3,7,7,9,9,15,11,18,18,21,21,30,24,34,34,38,38,50,42,55,55,
%T A321202 60,60,75,65,81,81,87,87,105,93,112,112,119,119,140,126,148,148,156,
%U A321202 156,180,164,189,189,198,198,225,207,235,235,245,245,275,255,286,286,297
%N A321202 Row sums of the irregular triangle A321201.
%C A321202 Total number of parts in the partitions of n into parts of size 2 and 3. - _Andrew Howroyd_, Nov 10 2018
%H A321202 Andrew Howroyd, <a href="/A321202/b321202.txt">Table of n, a(n) for n = 2..1000</a>
%H A321202 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (-1,1,3,2,-2,-3,-1,1,1).
%F A321202 a(n) = Sum_{k=1..2*A008615(n+2)} A321201(n, k),  n >= 2.
%F A321202 From _Andrew Howroyd_, Nov 10 2018: (Start)
%F A321202 G.f.: x^2*(1 + 2*x + 2*x^2)/((1 + x + x^2)^2*(1 + x)^2*(1 - x)^3).
%F A321202 a(n) = Sum_{k=0..floor(n/6)} 2*k + (n-6*k)/2 for even n.
%F A321202 a(n) = Sum_{k=0..floor((n-3)/6)} 2*k + 1 + (n-3-6*k)/2 for odd n.
%F A321202 (End)
%t A321202 row[n_] := Reap[Do[If[2 e2 + 3 e3 == n, Sow[{e2, e3}]], {e2, 0, n/2}, {e3, 0, n/3}]][[2, 1]];
%t A321202 a[n_] := row[n] // Flatten // Total;
%t A321202 Table[a[n], {n, 2, 100}] (* _Jean-François Alcover_, Nov 23 2018 *)
%o A321202 (PARI) Vec((1 + 2*x + 2*x^2)/((1 + x + x^2)^2*(1 + x)^2*(1 - x)^3) + O(x^60)) \\ _Andrew Howroyd_, Nov 10 2018
%Y A321202 Cf. A008615, A321201.
%K A321202 nonn
%O A321202 2,3
%A A321202 _Wolfdieter Lang_, Nov 05 2018
%E A321202 Terms a(27) and beyond from _Andrew Howroyd_, Nov 10 2018