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A175112 First differences of A175111.

%I A175112 #21 Apr 04 2024 09:50:05
%S A175112 1,120,1442,6840,21122,51000,105122,194040,330242,528120,804002,
%T A175112 1176120,1664642,2291640,3081122,4059000,5253122,6693240,8411042,
%U A175112 10440120,12816002,15576120,18759842,22408440,26565122,31275000,36585122
%N A175112 First differences of A175111.
%C A175112 Convolution of the finite sequence 1,116,967,1672,967,116,1 with A001752. Number of points in the standard root system of the D_5 lattice having L_oo norm n.
%H A175112 Vincenzo Librandi, <a href="/A175112/b175112.txt">Table of n, a(n) for n = 0..1000</a>
%H A175112 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,0,5,-4,1).
%F A175112 a(n) = 4*a(n-1) -5*a(n-2) +5*a(n-4) -4*a(n-5) +a(n-6), n>6.
%F A175112 a(n) = ((2*n+1)^5-(2*n-1)^5)/2+(-1)^n, n>0.
%F A175112 G.f.: (116*x+967*x^2+1672*x^3+967*x^4+116*x^5+x^6+1)/((1+x)*(1-x)^5).
%t A175112 CoefficientList[Series[(116*x + 967*x^2 + 1672*x^3 + 967*x^4 + 116*x^5 + x^6+1)/((1 + x)*(1 - x)^5), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%t A175112 LinearRecurrence[{4,-5,0,5,-4,1},{1,120,1442,6840,21122,51000,105122},30] (* _Harvey P. Dale_, Sep 12 2023 *)
%o A175112 (Magma) I:=[1, 120, 1442, 6840, 21122, 51000, 105122]; [n le 7 select I[n] else 4*Self(n-1) - 5*Self(n-2) + 5*Self(n-4) - 4*Self(n-5) + Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Dec 19 2012
%Y A175112 Cf. A110907, A117216, A175114.
%K A175112 easy,nonn
%O A175112 0,2
%A A175112 _R. J. Mathar_, Feb 13 2010