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%I #18 Sep 08 2022 08:45:51
%S 1,364,7448,51012,206896,620060,1527624,3281908,6373472,11454156,
%T 19360120,31134884,48052368,71639932,103701416,146340180,201982144,
%U 273398828,363730392,476508676,615680240,785629404,991201288,1237724852
%N First differences of A175113.
%C Convolution of the finite sequence 1,358,5279,11764,5279,358,1 with A000389. Number of points in the standard root system of the D_6 lattice having L_infinity norm n.
%H Vincenzo Librandi, <a href="/A175114/b175114.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F a(n)= 6*a(n-1) -15*a(n-2) +20*a(n-3) -15*a(n-4) +6*a(n-5) -a(n-6), n>6.
%F a(n) = ((2*n+1)^6-(2*n-1)^6)/2 = 4*n*(12*n^2+1)*(4*n^2+3), n>0. - _Bruno Berselli_, Dec 27 2010
%F G.f.: (358*x+5279*x^2+11764*x^3+5279*x^4+358*x^5+1+x^6)/(x-1)^6. - _R. J. Mathar_, Jan 03 2011
%t CoefficientList[Series[(358 x + 5279 x^2 + 11764 x^3 + 5279 x^4 + 358 x^5 + 1+x^6)/(x - 1)^6, {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 20 2012 *)
%o (Magma) I:=[1,364,7448,51012,206896,620060,1527624]; [n le 7 select I[n] else 6*Self(n-1)-15*Self(n-2)+20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2012
%Y Cf. A110907, A117216, A175112.
%K easy,nonn
%O 0,2
%A _R. J. Mathar_, Feb 13 2010
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