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Antidiagonal sums of square array A082025.
5

%I #21 Apr 07 2020 10:56:19

%S 1,5,16,39,79,157,190,337,407,705,742,1147,1235,1855,1836,2879,2691,

%T 4067,3752,5683,5005,7687,6670,10117,8595,12837,10950,15737,13461,

%U 19621,16494,23739,19925,28401,23788,34057,28077,39997,32842,47027,38309

%N Antidiagonal sums of square array A082025.

%H Alois P. Heinz, <a href="/A082190/b082190.txt">Table of n, a(n) for n = 1..100</a>

%p 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

%t dmax = 50 (* number of antidiagonals *);

%t a[1, 1] = 1; used = {1}; a[_, _] = 1;

%t 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[]]];

%t Do[If[EvenQ[d], Do[loop, {j, d, 1, -1}], Do[loop, {j, 1, d}]], {d, 2, dmax}];

%t Table[Sum[a[d - k + 1, k], {k, 1, d}], {d, 1, dmax}] (* _Jean-François Alcover_, Apr 07 2020 *)

%Y Cf. A082025, A082187, A082188, A082189.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Apr 07 2003

%E More terms from _R. J. Mathar_, May 06 2006

%E Edited and further terms from _Alois P. Heinz_, Oct 07 2009