A115274 a(n) = n + A115273(n), where A115273(n) = 0 for n = 1..3.

1, 2, 3, 5, 7, 6, 9, 12, 9, 13, 17, 12, 17, 22, 15, 21, 27, 18, 25, 32, 21, 29, 37, 24, 33, 42, 27, 37, 47, 30, 41, 52, 33, 45, 57, 36, 49, 62, 39, 53, 67, 42, 57, 72, 45, 61, 77, 48, 65, 82, 51, 69, 87, 54, 73, 92, 57, 77, 97, 60, 81, 102, 63, 85, 107, 66, 89, 112, 69, 93, 117

Offset: 1

Author

Zak Seidov, Jan 18 2006

Keywords

• nonn
• easy

Comments

Three arithmetic progressions interlaced: a(1..3) = 1..3 and d = a(n+3)-a(n) = 4,5,3.

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).

Crossrefs

Cf. A115273.

Programs

Maple

seq(op([1+4*j,2+5*j,3+3*j]),j=0..100); # Robert Israel, May 11 2015

Mathematica

Table[n+Floor[n/3]*Mod[n, 3], {n, 78}]
LinearRecurrence[{0,0,2,0,0,-1},{1,2,3,5,7,6},80] (* Harvey P. Dale, Aug 06 2021 *)

PARI

Vec(x*(3*x^4+3*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, May 11 2015

Formula

a(n) = n+floor(n/3)*(n mod 3), n = 1, 2, ...

a(n) = 2*a(n-3)-a(n-6). - Colin Barker, May 11 2015

G.f.: x*(3*x^4+3*x^3+3*x^2+2*x+1) / ((x-1)^2*(x^2+x+1)^2). - Colin Barker, May 11 2015

E.g.f.: (-5+12*x)*exp(x)/9 + (3+2*x)*sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/2)/9 + 5*exp(-x/2)*cos(sqrt(3)*x/2)/9. - Robert Israel, May 11 2015