A243520 Numbers that are congruent to {0, 8} mod 11.

0, 8, 11, 19, 22, 30, 33, 41, 44, 52, 55, 63, 66, 74, 77, 85, 88, 96, 99, 107, 110, 118, 121, 129, 132, 140, 143, 151, 154, 162, 165, 173, 176, 184, 187, 195, 198, 206, 209, 217, 220, 228, 231, 239, 242, 250, 253, 261, 264, 272, 275, 283, 286, 294, 297, 305

Offset: 0

Author

Viet Quoc Le Tran, Jun 14 2014

Keywords

• nonn
• easy

Comments

Union of A008593 and A017485. - Michel Marcus, Jun 15 2014

This sequence mimics in some sense the ceiling function of n/2 (the seq. A110654) relative to variations from a main class of recurrence relations; in order to get the ceiling function of n/2 (see Formula section), the vector v must be [0,1] instead of [3,8]. - R. J. Cano, Jun 15 2014

Links

• R. J. Cano, Table of n, a(n) for n = 0..9999
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A010706, A110654, A078707.

Programs

Magma

&cat [[11*n,11*n+8]: n in [0..30]]; // [Bruno Berselli, Jun 16 2014]

Maple

A243520:=n->5*n + 2*(n mod 2) + ceil(n/2); seq(A243520(n), n=0..50); # Wesley Ivan Hurt, Jun 21 2014

Mathematica

Flatten[Table[11 n + {0, 8}, {n, 0, 32}]] (* Alonso del Arte, Jun 15 2014 *)

PARI

a(n)=5*n+2*(n%2)+ceil(n/2); \\ R. J. Cano, Jun 15 2014

PARI

a(n)=if(!n,0,a(n-1)+[3,8][1+n%2]); \\ R. J. Cano, Jun 15 2014

Formula

a(n) = -5/4*(-1)^n + 11*n/2 + 5/4.

From R. J. Cano, Jun 15 2014: (Start)

a(n) = 5*n + 2*(n mod 2) + ceiling(n/2).

If n=0 then a(n) is zero, else a(n) = a(n-1) + v[n mod 2], where v is [3,8]. (End)

G.f.: x*(8 + 3*x) / ((1 + x)*(1 - x)^2). [Bruno Berselli, Jun 16 2014]

a(n) = sum( A010706(i), i=0..n ) - 3. [Bruno Berselli, Jun 16 2014]

E.g.f.: (11*x*exp(x) + 5*sinh(x))/2. - David Lovler, Sep 04 2022