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%I #18 May 03 2023 14:32:08
%S 1,1,1,2,2,3,4,4,6,7,10,12,16,19,24,28,34,39,46,52,60,67,76,84,94,103,
%T 114,124,136,147,160,172,186,199,214,228,244,259,276,292,310,327,346,
%U 364,384,403,424,444,466,487,510,532,556,579,604,628,654,679,706,732
%N a(1), a(2), a(3) = 1; a(n) = (a(n-1) mod a(n-3)) + a(n-2) + 1.
%H Matthew Niemiro, <a href="/A330715/b330715.txt">Table of n, a(n) for n = 1..1000</a>
%F a(1), a(2), a(3) = 1; a(n) = (a(n-1) mod a(n-3)) + a(n-2) + 1.
%F Conjectures from _Colin Barker_, Dec 28 2019: (Start)
%F G.f.: x*(1 - x - x^2 + 2*x^3 - x^4 + x^6 - 2*x^7 + 2*x^8) / ((1 - x)^3*(1 + x)).
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n>9.
%F a(n) = (99 - 3*(-1)^n - 24*n + 2*n^2) / 8 for n>5.
%F (End)
%t Nest[Append[#, Mod[#[[-1]], #[[-3]] ] + #[[-2]] + 1] &, {1, 1, 1}, 57] (* _Michael De Vlieger_, Dec 27 2019 *)
%o (Python)
%o x = 1
%o y = 1
%o z = 1
%o for i in range(4, 1001):
%o new = z % x + y + 1
%o print(str(i) +" " + str(new))
%o x = y
%o y = z
%o z = new
%K nonn,hear
%O 1,4
%A _Matthew Niemiro_, Dec 27 2019
%E More terms from _Michael De Vlieger_, Dec 27 2019
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