A080341 - OEIS

%I #17 May 30 2022 16:32:32

%S 1,5,10,17,27,38,51,67,84,103,125,148,173,201,230,261,295,330,367,407,

%T 448,491,537,584,633,685,738,793,851,910,971,1035,1100,1167,1237,1308,

%U 1381,1457,1534,1613,1695,1778,1863,1951,2040,2131,2225,2320,2417

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

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,1,-2,1).

%F 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.

%F G.f.: x*(1+3*x+x^2+x^3)/(1-x)^3/(1+x+x^2). [_Colin Barker_, Feb 12 2012]

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

%o (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)+" ");

%Y Cf. A047259.

%K easy,nonn

%O 1,2

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