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Expansion of (theta_3(z)*theta_3(21z) + theta_2(z)*theta_2(21z)).
1

%I #11 Feb 25 2020 23:44:24

%S 1,0,2,0,0,0,0,0,2,0,0,4,0,0,0,4,0,0,2,0,0,0,0,4,0,0,0,0,0,0,0,0,2,0,

%T 0,4,0,0,0,0,0,0,2,0,4,0,0,0,0,0,6,4,0,0,0,0,0,0,0,0,4,0,0,0,0,0,0,0,

%U 0,0,0,4,2,0,4,0,0,0,0,0,0

%N Expansion of (theta_3(z)*theta_3(21z) + theta_2(z)*theta_2(21z)).

%H Jinyuan Wang, <a href="/A028649/b028649.txt">Table of n, a(n) for n = 0..1000</a>

%t r[n_]:=Reduce[{x, y}.{{2, 1}, {1, 11}}.{x, y}==n, {x, y}, Integers]; Table[rn=r[n];Which[rn===False, 0, Head[rn]===Or, Length[rn], Head[rn]===And, 1], {n, 0, 105}] (* _Vincenzo Librandi_, Feb 23 2020 *)

%o (PARI) a(n) = if(n<1, n==0, qfrep([2, 1; 1, 11], n)[n]*2); \\ _Jinyuan Wang_, Feb 21 2020

%Y Cf. A028650, A028651, A028652.

%K nonn

%O 0,3

%A _N. J. A. Sloane_