A080341 Sum of the first n terms that are congruent to 1, 4 or 5 mod 6 (A047259).

1, 5, 10, 17, 27, 38, 51, 67, 84, 103, 125, 148, 173, 201, 230, 261, 295, 330, 367, 407, 448, 491, 537, 584, 633, 685, 738, 793, 851, 910, 971, 1035, 1100, 1167, 1237, 1308, 1381, 1457, 1534, 1613, 1695, 1778, 1863, 1951, 2040, 2131, 2225, 2320, 2417

Offset: 1

Author

Christian Mercat (Integer.Sequence(AT)entrelacs.net), Mar 20 2003

Keywords

• easy
• nonn

Comments

Number of edges needed in a sector of a hexagon of size n paved by rhombi coming from triangular/hexagonal lattices.

Links

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

Crossrefs

Cf. A047259.

Programs

Mathematica

Accumulate[Select[Range[100],MemberQ[{1,4,5},Mod[#,6]]&]] (* Harvey P. Dale, Aug 16 2012 *)

Formula

a(n) = n^2+(n+1)/3 with integer division, that is n mod 3 = 0 : n^2+n/3 n mod 3 = 1 : n^2+(n-1)/3 n mod 3 = 2 : n^2+(n+1)/3.

G.f.: x*(1+3*x+x^2+x^3)/(1-x)^3/(1+x+x^2). [Colin Barker, Feb 12 2012]