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A330082 a(n) = 5*A064038(n+1).

%I A330082 #34 Dec 05 2023 03:25:35
%S A330082 0,5,15,15,25,75,105,70,90,225,275,165,195,455,525,300,340,765,855,
%T A330082 475,525,1155,1265,690,750,1625,1755,945,1015,2175,2325,1240,1320,
%U A330082 2805,2975,1575,1665,3515,3705,1950,2050,4305,4515,2365,2475,5175,5405,2820,2940
%N A330082 a(n) = 5*A064038(n+1).
%C A330082 Main column of a pentagonal spiral for A026741:
%C A330082                        (25)
%C A330082                     49 (15) 31
%C A330082                 24  29 (15)  8  16
%C A330082             47  14   7 ( 5)  3  17  33
%C A330082         23  27  13   2 ( 0)  1   7   9  17
%C A330082           45  13   6   3   1   4  19  35
%C A330082             22  25  11   5   9  10  18
%C A330082               43  12  23  11  21  37
%C A330082                 21  41  20  39  19
%C A330082 a(n) = 5 * A064038(n+1) from a pentagonal spiral.
%C A330082 Compare to A319127 =  6 * A002620 in the hexagonal spiral:
%C A330082                 22  23  23  22 (24)
%C A330082               20  12  13  13 (12) 25
%C A330082             21  10   5   4 ( 6) 14  25
%C A330082           21  11   5   1 ( 0)  7  15  24
%C A330082         20  11   4   1 ( 0)  2   7  15  26
%C A330082           18  10   2   3   3   6  14  27
%C A330082             19   8   9   9   8  16  27
%C A330082               19  18  16  17  17  26
%C A330082                 30  28  29  29  28
%H A330082 Colin Barker, <a href="/A330082/b330082.txt">Table of n, a(n) for n = 0..1000</a>
%H A330082 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,-6,10,-12,12,-10,6,-3,1).
%F A330082 a(n) = A026741(A028895(n)).
%F A330082 From _Colin Barker_, Dec 08 2019: (Start)
%F A330082 G.f.: 5*x*(1 + 4*x^3 + x^6) / ((1 - x)^3*(1 + x^2)^3).
%F A330082 a(n) = 3*a(n-1) - 6*a(n-2) + 10*a(n-3) - 12*a(n-4) + 12*a(n-5) - 10*a(n-6) + 6*a(n-7) - 3*a(n-8) + a(n-9) for n>8.
%F A330082 a(n) = (-5/16 + (5*i)/16)*(((-3-3*i) + (-i)^n + i^(1+n))*n*(1+n)) where i=sqrt(-1).
%F A330082 (End)
%t A330082 A330082[n_]:=5Numerator[n(n+1)/4];Array[A330082,100,0] (* _Paolo Xausa_, Dec 04 2023 *)
%o A330082 (PARI) concat(0, Vec(5*x*(1 + 4*x^3 + x^6) / ((1 - x)^3*(1 + x^2)^3) + O(x^50))) \\ _Colin Barker_, Dec 08 2019
%Y A330082 Cf. A026741, A028895, A064038. A033429, A062786, A087348, A147874, A158447, A168668 are in the spiral.
%K A330082 nonn,easy
%O A330082 0,2
%A A330082 _Paul Curtz_, Dec 01 2019
%E A330082 More terms from _Colin Barker_, Dec 22 2019
%E A330082 Name corrected by _Paolo Xausa_, Dec 04 2023