A286159 Lower triangular region of array A286156, transposed.

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, 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, 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

Offset: 1

Author

Antti Karttunen, May 04 2017

Keywords

• nonn
• tabl

Examples

			The first ten rows of this triangular array:
  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, 13,  3, 12, 10, 36,
  1, 4, 8, 13, 19,  7,  6, 16, 45,
  1, 4, 8, 13, 19,  3, 12, 11, 15, 55
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10585; the first 145 rows of the triangle

Crossrefs

Transpose: A268158.

Cf. A000012, A000217, A268156, A268157.

Rows converge towards A034856.

Programs

Mathematica

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 *)

Python

def T(a, b): return ((a + b)**2 + 3*a + b)//2
def a(n, k): return T(n%k, n//k)
for n in range(1, 21): print([a(n , k) for k in range(1, n + 1)][::-1])  # Indranil Ghosh, May 20 2017

Scheme

(define (A286159 n) (A286156bi (A002024 n) (A004736 n))) ;; For A286156bi see A286156.