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A286158 Lower triangular region of array A286156.

%I A286158 #19 Jun 12 2025 13:00:05
%S A286158 1,3,1,6,4,1,10,3,4,1,15,7,8,4,1,21,6,3,8,4,1,28,11,7,13,8,4,1,36,10,
%T A286158 12,3,13,8,4,1,45,16,6,7,19,13,8,4,1,55,15,11,12,3,19,13,8,4,1,66,22,
%U A286158 17,18,7,26,19,13,8,4,1,78,21,10,6,12,3,26,19,13,8,4,1,91,29,16,11,18,7,34,26,19,13,8,4,1,105,28,23,17,25,12,3,34,26,19,13,8,4,1
%N A286158 Lower triangular region of array A286156.
%H A286158 Antti Karttunen, <a href="/A286158/b286158.txt">Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle</a>
%F A286158 A(n,k) = A286158(n,k) listed for n >= 1, k = 1 .. n.
%e A286158 The first ten rows of this triangular array:
%e A286158    1,
%e A286158    3,  1,
%e A286158    6,  4,  1,
%e A286158   10,  3,  4,  1,
%e A286158   15,  7,  8,  4,  1,
%e A286158   21,  6,  3,  8,  4,  1,
%e A286158   28, 11,  7, 13,  8,  4,  1,
%e A286158   36, 10, 12,  3, 13,  8,  4,  1,
%e A286158   45, 16,  6,  7, 19, 13,  8,  4,  1,
%e A286158   55, 15, 11, 12,  3, 19, 13,  8,  4,  1.
%t A286158 Map[((#1 + #2)^2 + 3 #1 + #2)/2 & @@ # & /@ Reverse@ # &, Table[Reverse@ QuotientRemainder[n, k], {n, 14}, {k, n, 1, -1}]] // Flatten (* _Michael De Vlieger_, May 20 2017 *)
%o A286158 (Scheme) (define (A286158 n) (A286156bi (A002024 n) (A002260 n))) ;; For A286156bi see A286156.
%o A286158 (Python)
%o A286158 def T(a, b): return ((a + b)**2 + 3*a + b)//2
%o A286158 def a(n, k): return T(n%k, n//k)
%o A286158 for n in range(1, 21): print([a(n, k) for k in range(1, n + 1)])  # _Indranil Ghosh_, May 20 2017
%Y A286158 Transpose: A286159.
%Y A286158 Cf. A000217 (left edge), A000012 (right edge).
%Y A286158 Cf. A286156.
%K A286158 nonn,tabl
%O A286158 1,2
%A A286158 _Antti Karttunen_, May 04 2017