A115010 Array read by antidiagonals: let V(m,n) = Sum_{i=1..m, j=1..n, gcd(i,j)=1} (m+1-i)*(n+1-j), then T(m,n) = 2*m*n+m+n+2*V(m,n), for m >= 1, n >= 1.

6, 13, 13, 22, 28, 22, 33, 49, 49, 33, 46, 74, 86, 74, 46, 61, 105, 131, 131, 105, 61, 78, 140, 188, 200, 188, 140, 78, 97, 181, 251, 289, 289, 251, 181, 97, 118, 226, 326, 386, 418, 386, 326, 226, 118, 141, 277, 409, 503, 559, 559, 503, 409, 277, 141, 166, 332, 502, 632, 730

Offset

1,1

Links

Table of n, a(n) for n=1..60.

Max A. Alekseyev, On the number of two-dimensional threshold functions, arXiv:math/0602511 [math.CO], 2006-2010; SIAM J. Disc. Math. 24(4), 2010, pp. 1617-1631. doi:10.1137/090750184

Maple

V:=proc(m, n) local t1, i, j; t1:=0; for i from 1 to m do for j from 1 to n do if gcd(i, j)=1 then t1:=t1+(m+1-i)*(n+1-j); fi; od; od; t1; end; T:=(m, n)->(2*m*n+m+n+2*V(m, n));

Mathematica

V[m_, n_] := Sum[Boole[CoprimeQ[i, j]]*(m-i+1)*(n-j+1), {i, m}, {j, n}];
T[m_, n_] := 2*m*n + m + n + 2*V[m, n];
Table[T[m - n + 1, n], {m, 1, 12}, {n, 1, m}] // Flatten (* Jean-François Alcover, Nov 28 2017 *)

Crossrefs

Cf. A114999, A114043, A115004, A115005, A115006, A115007.

Sequence in context: A265740 A090324 A106623 * A244535 A066826 A031113

Adjacent sequences: A115007 A115008 A115009 * A115011 A115012 A115013

Keyword

nonn,tabl

Author

N. J. A. Sloane, Feb 24 2006

Status

approved