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
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).
Programs
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Magma
&cat [[11*n,11*n+8]: n in [0..30]]; // [Bruno Berselli, Jun 16 2014]
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Maple
A243520:=n->5*n + 2*(n mod 2) + ceil(n/2); seq(A243520(n), n=0..50); # Wesley Ivan Hurt, Jun 21 2014
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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
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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
Comments