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A235537 Expansion of (6 + 13*x - 8*x^2 - 8*x^3 + 6*x^4)/((1 + x)^2*(1 - x)^3).

%I A235537 #25 Sep 08 2022 08:46:06
%S A235537 6,19,23,41,49,72,84,112,128,161,181,219,243,286,314,362,394,447,483,
%T A235537 541,581,644,688,756,804,877,929,1007,1063,1146,1206,1294,1358,1451,
%U A235537 1519,1617,1689,1792,1868,1976,2056,2169,2253,2371,2459,2582,2674,2802,2898
%N A235537 Expansion of (6 + 13*x - 8*x^2 - 8*x^3 + 6*x^4)/((1 + x)^2*(1 - x)^3).
%H A235537 Bruno Berselli, <a href="/A235537/b235537.txt">Table of n, a(n) for n = 0..1000</a>
%H A235537 Bruno Berselli, <a href="/A235537/a235537.jpg">Triangular spiral which contains the terms of A235537</a> (see A051682).
%H A235537 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A235537 G.f.: (6 + 13*x - 8*x^2 - 8*x^3 + 6*x^4)/((1 + x)^2*(1 - x)^3).
%F A235537 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F A235537 a(n) = (6*n*(3*n + 17) - (2*n + 43)*(-1)^n + 11)/16 + 8. The terms a(2k) are in A235332; the closed form of the terms a(2k+1) is n*(9*n+35)/2+19.
%t A235537 Table[(6 n (3 n + 17) - (2 n + 43) (-1)^n + 11)/16 + 8, {n, 0, 50}]
%t A235537 LinearRecurrence[{1,2,-2,-1,1},{6,19,23,41,49},80] (* _Harvey P. Dale_, Aug 22 2015 *)
%o A235537 (Magma) [(6*n*(3*n+17)-(2*n+43)*(-1)^n+11)/16+8: n in [0..50]];
%Y A235537 Cf. A235332.
%K A235537 nonn,easy
%O A235537 0,1
%A A235537 _Bruno Berselli_, Jan 23 2014