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

0,2

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).

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

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 *)

Prog

(PARI) a(n)=5*n+2*(n%2)+ceil(n/2); /* or */ a(n)=if(!n, 0, a(n-1)+[3, 8][1+n%2]); \\ R. J. Cano, Jun 15 2014
(Magma) &cat [[11*n, 11*n+8]: n in [0..30]]; // [Bruno Berselli, Jun 16 2014]

Crossrefs

Cf. A010706, A110654, A078707.

Sequence in context: A000852 A000873 A213084 * A129730 A347757 A368356

Adjacent sequences: A243517 A243518 A243519 * A243521 A243522 A243523

Keyword

nonn,easy

Author

Viet Quoc Le Tran, Jun 14 2014

Status

approved