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A332597 Number of edges in a "frame" of size n X n (see Comments in A331776 for definition). 2
8, 92, 360, 860, 1792, 3124, 5256, 8188, 12304, 17460, 24568, 33244, 44688, 58228, 74664, 94028, 118080, 145380, 178568, 216252, 259776, 308276, 365352, 428556, 501152, 580804, 670536, 768908, 880992, 1001764, 1138248, 1286748, 1449984, 1625300, 1817752, 2023740, 2252048, 2495476, 2759304, 3040460, 3349056 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A331776 for many other illustrations.

Theorem. Let z(n) = Sum_{i, j = 1..n, gcd(i,j)=1} (n+1-i)*(n+1-j) (this is A115004) and z_2(n) = Sum_{i, j = 1..n, gcd(i,j)=2} (n+1-i)*(n+1-j) (this is A331761). Then, for n >= 2, a(n) = 8*z(n) - 4*z_2(n) + 28*n^2 - 44*n + 8. - Scott R. Shannon and N. J. A. Sloane, Mar 06 2020

LINKS

Table of n, a(n) for n=1..41.

Scott R. Shannon, Colored illustration for a(3) = 360 (there are 360 edges in this picture).

MAPLE

V := proc(m, n, q) local a, i, j; a:=0;

for i from 1 to m do for j from 1 to n do

if gcd(i, j)=q then a:=a+(m+1-i)*(n+1-j); fi; od: od: a; end;

f := n -> if n=1 then 8 else 28*n^2 - 44*n + 8 + 8*V(n, n, 1) - 4*V(n, n, 2); fi;

[seq(f(n), n=1..50)]; # N. J. A. Sloane, Mar 10 2020

CROSSREFS

Cf. A115004, A331761, A331776 (regions), A332598 (vertices).

Sequence in context: A220573 A303743 A187157 * A331448 A215057 A222400

Adjacent sequences:  A332594 A332595 A332596 * A332598 A332599 A332600

KEYWORD

nonn

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Mar 02 2020

EXTENSIONS

More terms from N. J. A. Sloane, Mar 10 2020

STATUS

approved

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Last modified July 28 17:15 EDT 2021. Contains 346335 sequences. (Running on oeis4.)