cp's OEIS Frontend

A131818 A130296 + A002260 - A000012. Triangle read by rows: row n consists of n, 2, 3, 4, ..., n.

%I A131818 #15 Jul 07 2025 10:21:26
%S A131818 1,2,2,3,2,3,4,2,3,4,5,2,3,4,5,6,2,3,4,5,6,7,2,3,4,5,6,7,8,2,3,4,5,6,
%T A131818 7,8,9,2,3,4,5,6,7,8,9,10,2,3,4,5,6,7,8,9,10,11,2,3,4,5,6,7,8,9,10,11,
%U A131818 12,2,3,4,5,6,7,8,9,10,11,12
%N A131818 A130296 + A002260 - A000012. Triangle read by rows: row n consists of n, 2, 3, 4, ..., n.
%C A131818 Row sums = A034856; (1, 4, 8, 13, 19, 26, 34, ...).
%F A131818 A130296 + A002260 - A000012 as infinite lower triangular matrices.
%F A131818 T(n, 1) = n, T(n, k) = k for k > 1. - _Michel Marcus_, Feb 12 2014
%e A131818 First few rows of the triangle:
%e A131818   1;
%e A131818   2, 2;
%e A131818   3, 2, 3;
%e A131818   4, 2, 3, 4;
%e A131818   5, 2, 3, 4, 5;
%e A131818   6, 2, 3, 4, 5, 6;
%e A131818   7, 2, 3, 4, 5, 6, 7;
%e A131818   ...
%t A131818 Table[Join[{n},Range[2,n]],{n,15}]//Flatten (* _Harvey P. Dale_, Feb 24 2021 *)
%o A131818 (PARI) t(n, k) = if (k==1, n, k); \\ _Michel Marcus_, Feb 12 2014
%o A131818 (Python)
%o A131818 from math import isqrt, comb
%o A131818 def A131818(n):
%o A131818     y = (m:=isqrt(k:=n-1<<1))+(k>m*(m+1))
%o A131818     return n-comb(y,2) # _Chai Wah Wu_, Jul 07 2025
%Y A131818 Cf. A130296, A002260, A034856.
%K A131818 nonn,tabl
%O A131818 1,2
%A A131818 _Gary W. Adamson_, Jul 18 2007
%E A131818 More terms from _Michel Marcus_, Feb 12 2014