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

Author

Wolfdieter Lang, Nov 05 2018

Keywords

• nonn

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
• Index entries for linear recurrences with constant coefficients, signature (-1,1,3,2,-2,-3,-1,1,1).

Crossrefs

Cf. A008615, A321201.

Programs

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 *)

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

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)

Extensions

Terms a(27) and beyond from Andrew Howroyd, Nov 10 2018