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A115266
Row sums of correlation triangle for floor((n+3)/3).
3
1, 2, 4, 8, 13, 20, 31, 44, 61, 84, 111, 144, 186, 234, 291, 360, 438, 528, 634, 752, 886, 1040, 1210, 1400, 1615, 1850, 2110, 2400, 2715, 3060, 3441, 3852, 4299, 4788, 5313, 5880, 6496, 7154, 7861, 8624, 9436, 10304, 11236, 12224, 13276, 14400, 15588
OFFSET
0,2
COMMENTS
Row sums of number triangle A115265.
Sum of the smallest parts in all the partitions of k into 3 parts such that 3 <= k <= n+3. - Wesley Ivan Hurt, Nov 03 2021
FORMULA
G.f.: (1+x+x^2)^2/((1-x^3)^4*(1-x^2)).
a(n) = Sum_{k=0..n} Sum_{j=0..n} [j<=k]*floor((k-j+3)/3)*[j<=n-k]*floor((n-k-j+3)/3).
From Wesley Ivan Hurt, Nov 03 2021: (Start)
a(n) = Sum_{m=1..n+3} Sum_{k=1..floor(m/3)} Sum_{i=k..floor((m-k)/2)} k.
a(n) = 2*a(n-1)-3*a(n-4)+3*a(n-6)-2*a(n-9)+a(n-10). (End)
MATHEMATICA
T[n_, k_] := Sum[Boole[j <= k] * Floor[(k - j + 3)/3] * Boole[j <= n - k] * Floor[(n - k - j + 3)/3], {j, 0, n}]; a[n_] := Sum[T[n, k], {k, 0, n}]; Table[a[n], {n, 0, 46}] (* Jean-François Alcover, Jul 15 2017 *)
LinearRecurrence[{2, 0, 0, -3, 0, 3, 0, 0, -2, 1}, {1, 2, 4, 8, 13, 20, 31, 44, 61, 84}, 50] (* Harvey P. Dale, Nov 20 2021 *)
CROSSREFS
Cf. A115265.
Sequence in context: A164466 A164487 A130840 * A164508 A308094 A292774
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Jan 18 2006
STATUS
approved