A245621 Sequence of distinct least nonnegative numbers such that the average of the first n terms is a cube.
0, 2, 1, 29, 8, 122, 27, 323, 64, 674, 125, 1217, 216, 1994, 343, 3047, 512, 4418, 729, 6149, 1000, 8282, 1331, 10859, 1728, 13922, 2197, 17513, 2744, 21674, 3375, 26447, 4096, 31874, 4913, 37997, 5832, 44858, 6859, 52499, 8000, 60962, 9261, 70289, 10648, 80522, 12167, 91703, 13824
Offset: 1
Keywords
Programs
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PARI
v=[]; n=0; while(n<50000, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=0, n, if(i^3>(num/(#v+1)), break); if(i^3==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=0; break))); n++)
Formula
Conjecture: a(2*n+1) = n^3, a(2*n) = 7*n^3 - 9*n^2 + 5*n - 1.
Conjecture: a(n) = 4*a(n-2)-6*a(n-4)+4*a(n-6)-a(n-8) for n>8. - Colin Barker, Nov 05 2014
Empirical g.f.: x^2*(x^6+x^5+18*x^4+4*x^3+21*x^2+x+2) / ((x-1)^4*(x+1)^4). - Colin Barker, Nov 05 2014
Empirical first differences of A212763.