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%I #25 Nov 19 2021 12:51:53
%S 2,23,93,243,492,878,1432,2165,3123,4337,5810,7596,9726,12195,15065,
%T 18367,22088,26298,31028,36257,42063,48477,55470,63128,71482,80495,
%U 90261,100811,112100,124230,137232,151053,165803,181513,198122,215748,234422,254075
%N Sum of the largest two parts in the partitions of 4n into 4 parts with smallest part equal to 1.
%H Vincenzo Librandi, <a href="/A239186/b239186.txt">Table of n, a(n) for n = 1..1000</a>
%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*(10*x^6+39*x^5+61*x^4+76*x^3+49*x^2+19*x+2) / ((x-1)^4*(x^2+x+1)^2). - _Colin Barker_, Mar 12 2014
%F a(n) = 2*a(n-1)-a(n-2)+2*a(n-3)-4*a(n-4)+2*a(n-5)-a(n-6)+2*a(n-7)-a(n-8). - _Wesley Ivan Hurt_, Nov 19 2021
%e For a(n) add the numbers in the first two columns.
%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 + 1 + 1 + 1 9 + 4 + 2 + 1
%e 8 + 2 + 1 + 1 8 + 5 + 2 + 1
%e 7 + 3 + 1 + 1 7 + 6 + 2 + 1
%e 6 + 4 + 1 + 1 9 + 3 + 3 + 1
%e 5 + 5 + 1 + 1 8 + 4 + 3 + 1
%e 7 + 2 + 2 + 1 7 + 5 + 3 + 1
%e 5 + 1 + 1 + 1 6 + 3 + 2 + 1 6 + 6 + 3 + 1
%e 4 + 2 + 1 + 1 5 + 4 + 2 + 1 7 + 4 + 4 + 1
%e 3 + 3 + 1 + 1 5 + 3 + 3 + 1 6 + 5 + 4 + 1
%e 1 + 1 + 1 + 1 3 + 2 + 2 + 1 4 + 4 + 3 + 1 5 + 5 + 5 + 1
%e 4(1) 4(2) 4(3) 4(4) .. 4n
%e ------------------------------------------------------------------------
%e 2 23 93 243 .. a(n)
%t b[n_] := Sum[((4 n - 2 - i)*Floor[(4 n - 2 - i)/2] - i (4 n - 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*(10*x^6+39*x^5+61*x^4+76*x^3+49*x^2+19*x+2)/((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, A239059.
%K nonn,easy
%O 1,1
%A _Wesley Ivan Hurt_, Mar 11 2014
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