A287893 a(n) = floor(n*(n+2)/9).
0, 0, 0, 1, 2, 3, 5, 7, 8, 11, 13, 15, 18, 21, 24, 28, 32, 35, 40, 44, 48, 53, 58, 63, 69, 75, 80, 87, 93, 99, 106, 113, 120, 128, 136, 143, 152, 160, 168, 177, 186, 195, 205, 215, 224, 235, 245, 255, 266, 277, 288, 300, 312, 323, 336, 348, 360, 373, 386
Offset: 0
Examples
a(3) = (15-6)/9 = 1.
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,1,-2,1).
Programs
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Mathematica
Table[Floor[(n(n+2))/9],{n,0,60}] (* or *) LinearRecurrence[{2,-1,0,0,0,0,0,0,1,-2,1},{0,0,0,1,2,3,5,7,8,11,13},60] (* Harvey P. Dale, Jan 09 2023 *) -
PARI
concat(vector(3), Vec(x^3*(1 + x^3 - x^5 + 2*x^6 - x^7) / ((1 - x)^3*(1 + x + x^2)*(1 + x^3 + x^6)) + O(x^100))) \\ Colin Barker, Jun 02 2017
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PARI
a(n)=n*(n+2)\9 \\ Charles R Greathouse IV, Jun 06 2017
Formula
a(n) = (A005563(n) - A005563(n) mod 9)/9. Note that A005563(n) mod 9 has period 9: repeat [0, 3, 8, 6, 6, 8, 3, 0, 8].
From Colin Barker, Jun 02 2017: (Start)
G.f.: x^3*(1 + x^3 - x^5 + 2*x^6 - x^7) / ((1 - x)^3*(1 + x + x^2)*(1 + x^3 + x^6)).
a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11) for n>10.
(End)
a(n) = floor(n*(n+2)/9). - Alois P. Heinz, Jun 02 2017
Extensions
Definition simplified by Alois P. Heinz, Jun 02 2017
Comments