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%I #19 Dec 26 2019 16:48:11
%S 1,2,3,5,6,7,10,11,12,16,17,18,23,24,25,31,32,33,40,41,42,50,51,52,61,
%T 62,63,73,74,75,86,87,88,100,101,102,115,116,117,131,132,133,148,149,
%U 150,166,167,168,185,186,187,205,206,207,226,227,228,248,249,250,271
%N Write three numbers, skip one, write three, skip two, write three, skip three... and so on.
%C Union of A052905, A052905+1, and A052905+2. - _Ivan Neretin_, Aug 03 2016
%C First terms of the 3 repeated terms belong to A052905. - _Michael De Vlieger_, Aug 03 2016
%H Ivan Neretin, <a href="/A101882/b101882.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2,0,-1,1).
%F G.f.: x*(1+x+x^2-x^4-x^5)/ ((1+x+x^2)^2 * (1-x)^3). [Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009; checked and corrected by _R. J. Mathar_, Sep 16 2009]
%t Flatten@Table[(n^2 + 5 n - 4)/2 + {0, 1, 2}, {n, 20}] (* _Ivan Neretin_, Aug 03 2016 *)
%t Table[Range[#, # + 2] &[(n^2 + 7 n + 2)/2], {n, 0, 20}] // Flatten (* or *)
%t Rest@ CoefficientList[Series[x (1 + x + x^2 - x^4 - x^5)/((1 + x + x^2)^2 (1 - x)^3), {x, 0, 61}], x] (* _Michael De Vlieger_, Aug 03 2016 *)
%t LinearRecurrence[{1,0,2,-2,0,-1,1},{1,2,3,5,6,7,10},70] (* _Harvey P. Dale_, Dec 26 2019 *)
%o (PARI) a(n)=my(k=n%3); if(k==2, n^2+17*n-2, k==1, n^2+19*n-2, n^2+15*n)/18 \\ _Charles R Greathouse IV_, Aug 03 2016
%Y Cf. A000217, A052905, A101881, A101883.
%K easy,nonn
%O 1,2
%A Candace Mills (scorpiocand(AT)yahoo.com), Dec 19 2004
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