A130296 - OEIS

%I #14 Nov 09 2024 11:37:29

%S 1,2,1,3,1,1,4,1,1,1,5,1,1,1,1,6,1,1,1,1,1,7,1,1,1,1,1,1,8,1,1,1,1,1,

%T 1,1,9,1,1,1,1,1,1,1,1,10,1,1,1,1,1,1,1,1,1,11,1,1,1,1,1,1,1,1,1,1,12,

%U 1,1,1,1,1,1,1,1,1,1,1,13,1,1,1,1,1,1,1,1,1,1,1,1,14,1,1,1,1,1,1,1,1,1,1,1,1,1

%N Triangle read by rows: T[i,1]=i, T[i,j]=1 for 1 < j <= i = 1,2,3,...

%C This sequence was formerly named "reversals of A051340", but it is actually the truncation of A051340 to its lower left triangular part, re-indexed to start rows and columns with 1. - _M. F. Hasler_, Aug 15 2015

%F Truncation of A051340 to its lower left. By rows, "n" followed by (n-1) 1's. (1,2,3...) in the left border, all 1's in other columns.

%F A130296^2 = A130297.

%F a(n) = A004201(n) - A004201(n-1) for n>1. - _Reinhard Zumkeller_, Jul 16 2008

%e First few rows of the triangle are:

%e 1;

%e 2, 1;

%e 3, 1, 1;

%e 4, 1, 1, 1;

%e 5, 1, 1, 1, 1;

%e ...

%o (PARI) A130296(i,j)=if(j==1,i,j<=i) \\ The sequence should not be defined for j>i but it is used in several places as infinite square matrix with upper right part equal to zero. - _M. F. Hasler_, Aug 15 2015

%o (Python)

%o from math import isqrt

%o def A130296(n): return comb((m:=isqrt(k:=n<<1))+(k>m*(m+1)),2)-comb((m2:=isqrt(k-2))+(k-2>m2*(m2+1)),2)+1 # _Chai Wah Wu_, Nov 09 2024

%Y Cf. A051340, A130297, A005408 (row sums).

%K nonn,tabl,easy

%O 1,2

%A _Gary W. Adamson_, May 20 2007