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V(n,n^2), where V is the number of integer points in an n-dimensional sphere of Lee-radius n^2 centered at the origin.
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%I #12 Feb 13 2021 04:31:32

%S 3,41,1159,50049,2908411,212358985,18665359119,1917971421185,

%T 225555471838387,29871434052884841,4398867465890529303,

%U 712959801840558794625,126115813138335816685995

%N V(n,n^2), where V is the number of integer points in an n-dimensional sphere of Lee-radius n^2 centered at the origin.

%C Since V(n,d) is symmetric, we have V(n,n^2) = V(n^2,n).

%H Solomon W. Golomb and Lloyd R. Welch, <a href="https://www.jstor.org/stable/2099465">Perfect Codes in the Lee Metric and the Packing of Polyominoes</a>, SIAM Journal on Applied Mathematics Vol. 18, No. 2 (Mar. 1970), pp. 302-317.

%H Milan Janjić, <a href="https://arxiv.org/abs/1905.04465">On Restricted Ternary Words and Insets</a>, arXiv:1905.04465 [math.CO], 2019.

%F V(n,d) = Sum_{j=0..min(n,d)} 2^j * binomial(n,j)*binomial(d,j).

%F a(n) ~ exp(n-2) * (2*n)^(n - 3/2) / sqrt(Pi). - _Vaclav Kotesovec_, Feb 13 2021

%t Array[Sum[2^j*Binomial[#1, j] Binomial[#2, j], {j, 0, Min[#1, #2]}] & @@ {#, #^2} &, 13] (* _Michael De Vlieger_, Jul 05 2019 *)

%Y V(n, n) = A001850, V(n, 2n) = A026000 and V(n, 3n) = A026001.

%K easy,nonn

%O 2,1

%A _Antonio Campello_, Nov 04 2010