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A345018 For each n, append to the sequence n^2 consecutive integers, starting from n.

%I A345018 #31 Nov 05 2024 09:13:43
%S A345018 1,2,3,4,5,3,4,5,6,7,8,9,10,11,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,
%T A345018 19,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,
%U A345018 28,29,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41
%N A345018 For each n, append to the sequence n^2 consecutive integers, starting from n.
%C A345018 Irregular triangle read by rows T(n,k) in which row n lists the integers from n to n + n^2 - 1, with n >= 1.
%H A345018 Paolo Xausa, <a href="/A345018/b345018.txt">Table of n, a(n) for n = 1..10416</a> (rows 1..31 of the triangle, flattened)
%F A345018 T(n,k) = n + k - 1, with n >= 1 and 1 <= k <= n^2.
%e A345018 Written as an irregular triangle T(n,k) the sequence begins:
%e A345018   n\k|  1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16 ...
%e A345018   ---+---------------------------------------------------------------
%e A345018    1 |  1;
%e A345018    2 |  2,  3,  4,  5;
%e A345018    3 |  3,  4,  5,  6,  7,  8,  9, 10, 11;
%e A345018    4 |  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19;
%e A345018   ...
%p A345018 T:= n-> (t-> seq(n+i, i=0..t-1))(n^2):
%p A345018 seq(T(n), n=1..6);  # _Alois P. Heinz_, Nov 05 2024
%t A345018 Table[Range[n,n^2+n-1],{n,6}] (* _Paolo Xausa_, Sep 05 2023 *)
%o A345018 (PARI) row(n) = vector(n^2, k, n+k-1); \\ _Michel Marcus_, Jun 08 2021
%o A345018 (Python)
%o A345018 from sympy import integer_nthroot
%o A345018 def A345018(n): return n-1+(k:=(m:=integer_nthroot(3*n,3)[0])+(6*n>m*(m+1)*((m<<1)+1)))*(k*(3-(k<<1))+5)//6 # _Chai Wah Wu_, Nov 05 2024
%Y A345018 Column 1: A000027.
%Y A345018 Right border: A028387.
%Y A345018 Row lengths: A000290.
%Y A345018 Row sums: A255499.
%Y A345018 Cf. A064866, A074279.
%K A345018 nonn,tabf
%O A345018 1,2
%A A345018 _Paolo Xausa_, Jun 05 2021