A286157 Transpose of square array A286156.

1, 3, 2, 6, 1, 2, 10, 4, 5, 2, 15, 3, 1, 5, 2, 21, 7, 4, 9, 5, 2, 28, 6, 8, 1, 9, 5, 2, 36, 11, 3, 4, 14, 9, 5, 2, 45, 10, 7, 8, 1, 14, 9, 5, 2, 55, 16, 12, 13, 4, 20, 14, 9, 5, 2, 66, 15, 6, 3, 8, 1, 20, 14, 9, 5, 2, 78, 22, 11, 7, 13, 4, 27, 20, 14, 9, 5, 2, 91, 21, 17, 12, 19, 8, 1, 27, 20, 14, 9, 5, 2, 105, 29, 10, 18, 3, 13, 4, 35, 27, 20, 14, 9, 5, 2

Offset

1,2

Comments

See A286156.

Links

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

Formula

A(n,k) = A286156(k,n).

Example

The top left 15 X 15 corner of the array:
  1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78,  91, 105, 120
  2, 1, 4,  3,  7,  6, 11, 10, 16, 15, 22, 21,  29,  28,  37
  2, 5, 1,  4,  8,  3,  7, 12,  6, 11, 17, 10,  16,  23,  15
  2, 5, 9,  1,  4,  8, 13,  3,  7, 12, 18,  6,  11,  17,  24
  2, 5, 9, 14,  1,  4,  8, 13, 19,  3,  7, 12,  18,  25,   6
  2, 5, 9, 14, 20,  1,  4,  8, 13, 19, 26,  3,   7,  12,  18
  2, 5, 9, 14, 20, 27,  1,  4,  8, 13, 19, 26,  34,   3,   7
  2, 5, 9, 14, 20, 27, 35,  1,  4,  8, 13, 19,  26,  34,  43
  2, 5, 9, 14, 20, 27, 35, 44,  1,  4,  8, 13,  19,  26,  34
  2, 5, 9, 14, 20, 27, 35, 44, 54,  1,  4,  8,  13,  19,  26
  2, 5, 9, 14, 20, 27, 35, 44, 54, 65,  1,  4,   8,  13,  19
  2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77,  1,   4,   8,  13
  2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90,   1,   4,   8
  2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104,   1,   4
  2, 5, 9, 14, 20, 27, 35, 44, 54, 65, 77, 90, 104, 119,   1

Mathematica

Map[((#1 + #2)^2 + 3 #1 + #2)/2 & @@ # & /@ Reverse@ # &, Table[Function[m, Reverse@ QuotientRemainder[m, k]][n - k + 1], {n, 14}, {k, n, 1, -1}]] // Flatten (* Michael De Vlieger, May 20 2017 *)

Prog

(Scheme) (define (A286157 n) (A286156bi (A004736 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(n - k + 1, k) for k in range(1, n + 1)] # Indranil Ghosh, May 20 2017

Crossrefs

Transpose: A286156.

Sequence in context: A209269 A373562 A244823 * A016460 A248645 A344323

Adjacent sequences: A286154 A286155 A286156 * A286158 A286159 A286160

Keyword

nonn,tabl

Author

Antti Karttunen, May 04 2017

Status

approved