A286159 - OEIS

%I #20 Dec 07 2019 12:18:29

%S 1,1,3,1,4,6,1,4,3,10,1,4,8,7,15,1,4,8,3,6,21,1,4,8,13,7,11,28,1,4,8,

%T 13,3,12,10,36,1,4,8,13,19,7,6,16,45,1,4,8,13,19,3,12,11,15,55,1,4,8,

%U 13,19,26,7,18,17,22,66,1,4,8,13,19,26,3,12,6,10,21,78,1,4,8,13,19,26,34,7,18,11,16,29,91,1,4,8,13,19,26,34,3,12,25,17,23,28,105

%N Lower triangular region of array A286156, transposed.

%H Antti Karttunen, <a href="/A286159/b286159.txt">Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle</a>

%e The first ten rows of this triangular array:

%e   1,

%e   1, 3,

%e   1, 4, 6,

%e   1, 4, 3, 10,

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

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

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

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

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

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

%t Map[((#1 + #2)^2 + 3 #1 + #2)/2 & @@ # & /@ Reverse@ # &, Table[Reverse@ QuotientRemainder[n, k], {n, 14}, {k, n}]] // Flatten (* _Michael De Vlieger_, May 20 2017 *)

%o (Scheme) (define (A286159 n) (A286156bi (A002024 n) (A004736 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(n , k) for k in range(1, n + 1)][::-1]  # _Indranil Ghosh_, May 20 2017

%Y Transpose: A268158.

%Y Cf. A000012, A000217, A268156, A268157.

%Y Rows converge towards A034856.

%K nonn,tabl

%O 1,3

%A _Antti Karttunen_, May 04 2017