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

1,2

Comments

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

Links

Table of n, a(n) for n=1..49.

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

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]

Mathematica

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

Prog

(Java or beanShell script) for(int i=1, s=m=0; i<40; i++) { m= i%6; if((m==1)||(m==4)||(m==5)) System.out.print((s+=i)+", "); } for(int i=1; i<20; i++) System.out.print((i*i+(i+1)/3)+" ");

Crossrefs

Cf. A047259.

Sequence in context: A034676 A076598 A306011 * A271328 A086653 A215449

Adjacent sequences: A080338 A080339 A080340 * A080342 A080343 A080344

Keyword

easy,nonn

Author

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

Status

approved