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%I #14 Sep 08 2022 08:45:49
%S 1,3,5,13,21,39,57,89,121,171,221,293,365,463,561,689,817,979,1141,
%T 1341,1541,1783,2025,2313,2601,2939,3277,3669,4061,4511,4961,5473,
%U 5985,6563,7141,7789,8437,9159,9881,10681,11481,12363,13245,14213,15181,16239,17297
%N First number in the n-th row of A172002.
%H Harvey P. Dale, <a href="/A168388/b168388.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -4, 1, 2, -1).
%F a(2*n+1) = A166464(n) a(2*n) = A166911(n).
%F a(n+1) - a(n) = A093907(n-1), n>1.
%F a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6).
%F G.f.: x*(1 - x^2 + 2*x)*(1 - x + x^2 + x^3)/( (1+x)^2 * (x-1)^4).
%F a(n+1) = A168380(n)+1.
%F From _G. C. Greubel_, Jul 19 2016: (Start)
%F a(n) = (12 + n + 3*(-1)^n*n + 2*n^3)/12.
%F E.g.f.: (1/12)*( -3*x - 12*exp(x) + (12 + 3*x + 6*x^2 + 2*x^3)*exp(2*x) )*exp(-x). (End)
%t LinearRecurrence[{2,1,-4,1,2,-1},{1,3,5,13,21,39},50] (* _Harvey P. Dale_, Nov 29 2014 *)
%t Table[(n + 1) (3 + 2 n^2 + 4 n - 3 (-1)^n)/12 + 1, {n, 0, 46}] (* _Michael De Vlieger_, Jul 19 2016, after _Vincenzo Librandi_ at A168380 *)
%o (Magma) [(12+n+3*(-1)^n*n+2*n^3)/12: n in [1..60]]; // _Vincenzo Librandi_, Jul 20 2016
%Y Cf. A168234.
%K nonn,easy
%O 1,2
%A _Paul Curtz_, Nov 24 2009
%E Edited and extended by _R. J. Mathar_, Mar 25 2010
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