A302302 Number of triples (i,j,k) such that i+j+k > 0 with -n <= i,j,k <= n.

0, 10, 53, 153, 334, 620, 1035, 1603, 2348, 3294, 4465, 5885, 7578, 9568, 11879, 14535, 17560, 20978, 24813, 29089, 33830, 39060, 44803, 51083, 57924, 65350, 73385, 82053, 91378, 101384, 112095, 123535, 135728, 148698, 162469, 177065, 192510, 208828, 226043

Offset: 0

Author

Andres Cicuttin, Apr 05 2018

Keywords

• nonn
• easy

Comments

If we add the triples (i,j,k) such that i+j+k >= 0 then the corresponding numbers seem to be those of A130748.

Links

• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1)

Crossrefs

Cf. A003215, A130748.

Programs

Mathematica

a[n_]:=Total[Flatten[Table[Table[Table[If[i+j+k>0,1,0],{i,-n,n}],{j,-n,n}],{k,-n,n}]]];
Table[a[n],{n,0,32}]

PARI

a(n) = n*(3+9*n+8*n^2)/2; \\ Altug Alkan, Apr 08 2018

Formula

From Alois P. Heinz, Apr 08 2018: (Start)

a(n) = n*(3+9*n+8*n^2)/2.

G.f.: (x^2+13*x+10)*x/(x-1)^4.

a(n) = A130748(n) - A003215(n) for n > 0. (End)