A181675 - OEIS

A181675

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.

3, 41, 1159, 50049, 2908411, 212358985, 18665359119, 1917971421185, 225555471838387, 29871434052884841, 4398867465890529303, 712959801840558794625, 126115813138335816685995

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OFFSET

2,1

COMMENTS

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

LINKS

Table of n, a(n) for n=2..14.

Solomon W. Golomb and Lloyd R. Welch, Perfect Codes in the Lee Metric and the Packing of Polyominoes, SIAM Journal on Applied Mathematics Vol. 18, No. 2 (Mar. 1970), pp. 302-317.

Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.

FORMULA

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

a(n) ~ exp(n-2) * (2*n)^(n - 3/2) / sqrt(Pi). - Vaclav Kotesovec, Feb 13 2021

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A222524 A241704 A380752 * A012053 A012162 A012225

Adjacent sequences: A181672 A181673 A181674 * A181676 A181677 A181678

KEYWORD

easy,nonn

AUTHOR

Antonio Campello, Nov 04 2010

STATUS

approved