A228921 Number of solutions to Sum_{i=1..n} x_i^2 == 0 (mod 8) with x_i in 0..7.
2, 8, 32, 128, 3072, 32768, 294912, 2392064, 17825792, 134217728, 1040187392, 8313110528, 67645734912, 549755813888, 4432406249472, 35461397479424, 282574488338432, 2251799813685248, 17979214137393152, 143833163343331328, 1151795604700004352, 9223372036854775808
Offset: 1
Links
- Colin Barker, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (16,-96,256,-256,4096,-24576,65536).
Programs
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Mathematica
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] -
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]<
Charles R Greathouse IV, Sep 15 2013 -
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
Formula
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
Extensions
a(10)-a(22) from Charles R Greathouse IV, Sep 15 2013