A082190 Antidiagonal sums of square array A082025.

1, 5, 16, 39, 79, 157, 190, 337, 407, 705, 742, 1147, 1235, 1855, 1836, 2879, 2691, 4067, 3752, 5683, 5005, 7687, 6670, 10117, 8595, 12837, 10950, 15737, 13461, 19621, 16494, 23739, 19925, 28401, 23788, 34057, 28077, 39997, 32842, 47027, 38309

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

Maple

b:= proc(t) option remember; false end: b(1):= true: ncpr:= proc() local i, m; m:= args[1]; for i from 2 to nargs do if igcd (m, args[i])<>1 then return true fi od; false end: T:= proc(n, k) option remember; local h, t, l; if n<1 or k<1 or n=1 and k=1 then t:=1 else h:= 1- 2* irem(n+k, 2); l:= T(n-1, k), T(n, k-1), T(n-1, k-1), T(n+h, k-h); for t while b(t) or ncpr(t, l) do od fi; b(t):= true; t end: seq(add(T(n, 1+d-n), n=1..d), d=1..60); # Alois P. Heinz, Oct 07 2009

Mathematica

dmax = 50 (* number of antidiagonals *);
a[1, 1] = 1; used = {1}; a[_, _] = 1;
loop := For[i = d - j + 1; k = 1, True, k++, If[FreeQ[used, k] && AllTrue[ {a[i - 1, j + 1], a[i - 1, j], a[i - 1, j - 1], a[i, j - 1], a[i + 1, j - 1]}, CoprimeQ[k, #] &], AppendTo[used, k]; a[i, j] = k; Break[]]];
Do[If[EvenQ[d], Do[loop, {j, d, 1, -1}], Do[loop, {j, 1, d}]], {d, 2, dmax}];
Table[Sum[a[d - k + 1, k], {k, 1, d}], {d, 1, dmax}] (* Jean-François Alcover, Apr 07 2020 *)

Crossrefs

Cf. A082025, A082187, A082188, A082189.

Sequence in context: A357289 A131283 A082199 * A155965 A216173 A269747

Adjacent sequences: A082187 A082188 A082189 * A082191 A082192 A082193

Keyword

nonn

Author

Amarnath Murthy, Apr 07 2003

Extensions

More terms from R. J. Mathar, May 06 2006

Edited and further terms from Alois P. Heinz, Oct 07 2009

Status

approved