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%I #31 Jan 08 2018 01:36:24
%S 1,2,8,11,23,28,46,53,77,86,116,127,163,176,218,233,281,298,352,371,
%T 431,452,518,541,613,638,716,743,827,856,946,977,1073,1106,1208,1243,
%U 1351,1388,1502,1541,1661,1702,1828,1871,2003,2048,2186,2233,2377,2426,2576
%N Even central polygonal numbers (A193868) divided by 2.
%C Central terms of A170950, seen as a triangle of rows with an odd number of terms.
%C Equivalently, numbers of the form m*(4*m+3)+1, where m = 0, -1, 1, -2, 2, -3, 3, ... [_Bruno Berselli_, Jan 05 2016]
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F a(n+3) - a(n+2) - a(n+1) + a(n) = A010696(n+1).
%F a(n) = A170950(A002061(n)).
%F a(n) = A193868(n)/2. - _Omar E. Pol_, Aug 16 2011
%F G.f. -x*(1+x+4*x^2+x^3+x^4) / ( (1+x)^2*(x-1)^3 ). - _R. J. Mathar_, Aug 18 2011
%t Select[Table[(n (n + 1)/2 + 1)/2, {n, 600}], IntegerQ] (* _Vladimir Joseph Stephan Orlovsky_, Feb 06 2012 *)
%t (Select[PolygonalNumber@ Range@ 100, OddQ] + 1 )/2 (* Version 10.4, or *)
%t Rest@ CoefficientList[Series[-x (1 + x + 4 x^2 + x^3 + x^4)/((1 + x)^2 (x - 1)^3), {x, 0, 50}], x] (* _Michael De Vlieger_, Jun 30 2016 *)
%o (PARI) a(n)=(2*n-1)*(2*n-1-(-1)^n)\4+1 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y Cf. A002522.
%Y Cf. A033951: numbers of the form m*(4*m+3)+1 for nonnegative m.
%K nonn,easy
%O 1,2
%A _Reinhard Zumkeller_, Mar 08 2010
%E New name from _Omar E. Pol_, Aug 16 2011
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