A321202 Row sums of the irregular triangle A321201.

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

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: (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

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