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%I #26 Jan 01 2018 21:24:53
%S 2,9,27,61,108,178,276,395,549,743,966,1236,1558,1917,2335,2817,3344,
%T 3942,4616,5343,6153,7051,8010,9064,10218,11441,12771,14213,15732,
%U 17370,19132,20979,22957,25071,27278,29628,32126,34725,37479,40393,43416,46606,49968
%N Sum of the two smallest parts from the partitions of 4n into 4 parts with smallest part = 1.
%H Iain Fox, <a href="/A239059/b239059.txt">Table of n, a(n) for n = 1..10000</a> (first 200 terms from Vincenzo Librandi)
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,2,-4,2,-1,2,-1).
%F G.f.: -x*(x^2+x+2)*(2*x^4-3*x^3-4*x^2-2*x-1) / ((x-1)^4*(x^2+x+1)^2). - _Colin Barker_, Mar 10 2014
%e For a(n) add the smallest two parts in the partitions with smallest part equal to 1..
%e 13 + 1 + 1 + 1
%e 12 + 2 + 1 + 1
%e 11 + 3 + 1 + 1
%e 10 + 4 + 1 + 1
%e 9 + 5 + 1 + 1
%e 8 + 6 + 1 + 1
%e 7 + 7 + 1 + 1
%e 11 + 2 + 2 + 1
%e 10 + 3 + 2 + 1
%e 9 + 4 + 2 + 1
%e 8 + 5 + 2 + 1
%e 7 + 6 + 2 + 1
%e 9 + 3 + 3 + 1
%e 8 + 4 + 3 + 1
%e 7 + 5 + 3 + 1
%e 6 + 6 + 3 + 1
%e 7 + 4 + 4 + 1
%e 6 + 5 + 4 + 1
%e 5 + 5 + 5 + 1
%e 9 + 1 + 1 + 1 10 + 2 + 2 + 2
%e 8 + 2 + 1 + 1 9 + 3 + 2 + 2
%e 7 + 3 + 1 + 1 8 + 4 + 2 + 2
%e 6 + 4 + 1 + 1 7 + 5 + 2 + 2
%e 5 + 5 + 1 + 1 6 + 6 + 2 + 2
%e 7 + 2 + 2 + 1 8 + 3 + 3 + 2
%e 6 + 3 + 2 + 1 7 + 4 + 3 + 2
%e 5 + 4 + 2 + 1 6 + 5 + 3 + 2
%e 5 + 3 + 3 + 1 6 + 4 + 4 + 2
%e 4 + 4 + 3 + 1 5 + 5 + 4 + 2
%e 5 + 1 + 1 + 1 6 + 2 + 2 + 2 7 + 3 + 3 + 3
%e 4 + 2 + 1 + 1 5 + 3 + 2 + 2 6 + 4 + 3 + 3
%e 3 + 3 + 1 + 1 4 + 4 + 2 + 2 5 + 5 + 3 + 3
%e 3 + 2 + 2 + 1 4 + 3 + 3 + 2 5 + 4 + 4 + 3
%e 1 + 1 + 1 + 1 2 + 2 + 2 + 2 3 + 3 + 3 + 3 4 + 4 + 4 + 4
%e 4(1) 4(2) 4(3) 4(4) .. 4n
%e ------------------------------------------------------------------------
%e 2 9 27 61 .. a(n)
%t b[n_] := Sum[((i + 2) (Floor[(4 n - 2 - i)/2] - i)) (Floor[(Sign[(Floor[(4 n - 2 - i)/2] - i)] + 2)/2]), {i, 0, 2 n}]; Table[b[n], {n, 50}]
%o (PARI) Vec(-x*(x^2+x+2)*(2*x^4-3*x^3-4*x^2-2*x-1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ _Colin Barker_, Sep 22 2014
%Y Cf. A238328, A238340, A238702, A238705, A238706, A239056, A239057.
%K nonn,easy
%O 1,1
%A _Wesley Ivan Hurt_, Mar 09 2014
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