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%I #27 Dec 21 2019 18:18:37
%S 2,8,32,128,3072,32768,294912,2392064,17825792,134217728,1040187392,
%T 8313110528,67645734912,549755813888,4432406249472,35461397479424,
%U 282574488338432,2251799813685248,17979214137393152,143833163343331328,1151795604700004352,9223372036854775808
%N Number of solutions to Sum_{i=1..n} x_i^2 == 0 (mod 8) with x_i in 0..7.
%H Colin Barker, <a href="/A228921/b228921.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (16,-96,256,-256,4096,-24576,65536).
%F G.f.: -2*x*(28672*x^6-9216*x^5+1280*x^4-64*x^3+48*x^2-12*x+1) / ((8*x-1)*(32*x^2-8*x+1)*(256*x^4+1)). - _Colin Barker_, Nov 10 2014
%t a[n_]:= a[n]=16 a[n-1]-96 a[n-2] + 256 a[n-3]-256 a[n-4]+4096a[n-5]-24576a[n-6]+ 65536 a[n-7];Do[a[i] = {2, 8, 32, 128, 3072, 32768, 294912}[[i]], {i, 1, 7}];Array[a,33]
%o (PARI) a(n)=my(v=vector(8,i,i==1)); for(i=1,n,v+=[2*v[8]+v[5], 2*v[1]+v[6], 2*v[2]+v[7], 2*v[3]+v[8], 2*v[4]+v[1], 2*v[5]+v[2], 2*v[6]+v[3], 2*v[7]+v[4]]); v[1]<<n \\ _Charles R Greathouse IV_, Sep 15 2013
%o (PARI) Vec(-2*x*(28672*x^6-9216*x^5+1280*x^4-64*x^3+48*x^2-12*x+1)/((8*x-1)*(32*x^2-8*x+1)*(256*x^4+1)) + O(x^100)) \\ _Colin Barker_, Nov 10 2014
%Y Cf. A228920, A229138, A229136.
%K nonn,easy
%O 1,1
%A _José María Grau Ribas_, Sep 15 2013
%E a(10)-a(22) from _Charles R Greathouse IV_, Sep 15 2013
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