A377809 k*(k+3)/2 appears k times.
2, 5, 5, 9, 9, 9, 14, 14, 14, 14, 20, 20, 20, 20, 20, 27, 27, 27, 27, 27, 27, 35, 35, 35, 35, 35, 35, 35, 44, 44, 44, 44, 44, 44, 44, 44, 54, 54, 54, 54, 54, 54, 54, 54, 54, 65, 65, 65, 65, 65, 65, 65, 65, 65, 65, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 77, 90
Offset: 1
Examples
As triangle: 2; 5, 5; 9, 9, 9; 14, 14, 14, 14; 20, 20, 20, 20, 20; ...
Programs
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Mathematica
s={};Do[AppendTo[s,Table[k(k+3)/2,k]],{k,12}];Flatten[s] (* James C. McMahon, Nov 09 2024 *) -
Python
from math import isqrt def A377809(n): return (r:=(m:=isqrt(k:=n<<1))+(k>m*(m+1)))*(r+3)>>1
Formula
First difference of A119713.
T(n,k) = A000096(n) for 1 <= k <= n. - Alois P. Heinz, Nov 09 2024
G.f.: x*y*(2 - x*y)/((1 - x)*(1 - x*y)^3). - Stefano Spezia, Nov 09 2024