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 A321202 Row sums of the irregular triangle A321201. 3
 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, 60, 60, 75, 65, 81, 81, 87, 87, 105, 93, 112, 112, 119, 119, 140, 126, 148, 148, 156, 156, 180, 164, 189, 189, 198, 198, 225, 207, 235, 235, 245, 245, 275, 255, 286, 286, 297 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,3 COMMENTS Total number of parts in the partitions of n into parts of size 2 and 3. - Andrew Howroyd, Nov 10 2018 LINKS Andrew Howroyd, Table of n, a(n) for n = 2..1000 FORMULA a(n) = Sum_{k=1..2*A008615(n+2)} A321201(n, k),  n >= 2. From Andrew Howroyd, Nov 10 2018 G.f.: x^2*(1 + 2*x + 2*x^2)/((1 + x + x^2)^2*(1 + x)^2*(1 - x)^3). a(n) = Sum_{k=0..floor(n/6)} 2*k + (n-6*k)/2 for even n. a(n) = Sum_{k=0..floor((n-3)/6)} 2*k + 1 + (n-3-6*k)/2 for odd n. (End) MATHEMATICA row[n_] := Reap[Do[If[2 e2 + 3 e3 == n, Sow[{e2, e3}]], {e2, 0, n/2}, {e3, 0, n/3}]][[2, 1]]; a[n_] := row[n] // Flatten // Total; Table[a[n], {n, 2, 100}] (* Jean-François Alcover, Nov 23 2018 *) PROG (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 CROSSREFS Cf. A008615, A321201. Sequence in context: A239665 A178179 A284833 * A308160 A151729 A088652 Adjacent sequences:  A321199 A321200 A321201 * A321203 A321204 A321205 KEYWORD nonn AUTHOR Wolfdieter Lang, Nov 05 2018 EXTENSIONS Terms a(27) and beyond from Andrew Howroyd, Nov 10 2018 STATUS approved

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Last modified July 21 17:20 EDT 2019. Contains 325198 sequences. (Running on oeis4.)