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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
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
FORMULA
a(n) = Sum_{k=1..2*A008615(n+2)} A321201(n, k), n >= 2.
From Andrew Howroyd, Nov 10 2018: (Start)
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
Sequence in context: A239665 A178179 A284833 * A308160 A151729 A088652
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Nov 05 2018
EXTENSIONS
Terms a(27) and beyond from Andrew Howroyd, Nov 10 2018
STATUS
approved