A130297 - OEIS

%I #7 Nov 09 2024 11:36:27

%S 1,4,1,8,2,1,13,3,2,1,19,4,3,2,1,26,5,4,3,2,1,34,6,5,4,3,2,1,43,7,6,5,

%T 4,3,2,1,53,8,7,6,5,4,3,2,1,64,9,8,7,6,5,4,3,2,1

%N A130296^2.

%C Left border = A034856: (1, 4, 8, 13, 19, 26, 34, ...).

%C Row sums = A028387: (1, 5, 11, 19, 29, 41, 55, ...).

%F Square of A130296 as an infinite lower triangular matrix.

%e First few rows of the triangle:

%e    1;

%e    4, 1;

%e    8, 2, 1;

%e   13, 3, 2, 1;

%e   19, 4, 3, 2, 1;

%e   26, 5, 4, 3, 2, 1;

%e   ...

%o (Python)

%o from math import comb, isqrt

%o def A130297(n): return (a:=comb(r:=(m:=isqrt(k:=n<<1))+(k>m*(m+1))+1,2))+1-n+(a-1 if ((k2:=n-1<<1)==(m2:=isqrt(k2))*(m2+1)) else 0) # _Chai Wah Wu_, Nov 09 2024

%Y Cf. A130296, A034856, A028387.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, May 20 2007