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%I #21 Jan 09 2023 18:28:44
%S 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,
%T 80,87,93,99,106,113,120,128,136,143,152,160,168,177,186,195,205,215,
%U 224,235,245,255,266,277,288,300,312,323,336,348,360,373,386
%N a(n) = floor(n*(n+2)/9).
%H Colin Barker, <a href="/A287893/b287893.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,0,0,0,1,-2,1).
%F 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].
%F Interleave A240438(n+1), A262523(n), A005563(n).
%F From _Colin Barker_, Jun 02 2017: (Start)
%F 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)).
%F a(n) = 2*a(n-1) - a(n-2) + a(n-9) - 2*a(n-10) + a(n-11) for n>10.
%F (End)
%F a(n) = floor(n*(n+2)/9). - _Alois P. Heinz_, Jun 02 2017
%e a(3) = (15-6)/9 = 1.
%t 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 *)
%o (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
%o (PARI) a(n)=n*(n+2)\9 \\ _Charles R Greathouse IV_, Jun 06 2017
%Y Cf. A005563, A240438, A262523, A262397, A262997.
%K nonn,easy
%O 0,5
%A _Paul Curtz_, Jun 02 2017
%E Definition simplified by _Alois P. Heinz_, Jun 02 2017
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