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Lower triangular region of array A286156.
3

%I #15 Dec 07 2019 12:18:29

%S 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 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 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 Lower triangular region of array A286156.

%H 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 A(n,k) = A286158(n,k) listed for n >= 1, k = 1 .. n.

%e The first ten rows of this triangular array:

%e 1,

%e 3, 1,

%e 6, 4, 1,

%e 10, 3, 4, 1,

%e 15, 7, 8, 4, 1,

%e 21, 6, 3, 8, 4, 1,

%e 28, 11, 7, 13, 8, 4, 1,

%e 36, 10, 12, 3, 13, 8, 4, 1,

%e 45, 16, 6, 7, 19, 13, 8, 4, 1,

%e 55, 15, 11, 12, 3, 19, 13, 8, 4, 1.

%t 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 (Scheme) (define (A286158 n) (A286156bi (A002024 n) (A002260 n))) ;; For A286156bi see A286156.

%o (Python)

%o def T(a, b): return ((a + b)**2 + 3*a + b)/2

%o def A(n, k): return T(n%k, int(n/k))

%o for n in range(1, 21): print [A(k, n - k + 1) for k in range(1, n + 1)] # _Indranil Ghosh_, May 20 2017

%Y Transpose: A286159.

%Y Cf. A000217 (left edge), A000012 (right edge).

%Y Cf. A286156.

%K nonn,tabl

%O 1,2

%A _Antti Karttunen_, May 04 2017