A286158 Lower triangular region of array A286156.

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, 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, 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

Offset

1,2

Links

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

Formula

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

Example

The first ten rows of this triangular array:
   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, 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.

Mathematica

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 *)

Prog

(Scheme) (define (A286158 n) (A286156bi (A002024 n) (A002260 n))) ;; For A286156bi see A286156.
(Python)
def T(a, b): return ((a + b)**2 + 3*a + b)/2
def A(n, k): return T(n%k, int(n/k))
for n in range(1, 21): print [A(k, n - k + 1) for k in range(1, n + 1)]  # Indranil Ghosh, May 20 2017

Crossrefs

Transpose: A286159.

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

Cf. A286156.

Sequence in context: A120029 A201904 A133110 * A185915 A086270 A325000

Adjacent sequences: A286155 A286156 A286157 * A286159 A286160 A286161

Keyword

nonn,tabl

Author

Antti Karttunen, May 04 2017

Status

approved