login
A286157
Transpose of square array A286156.
2
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.
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
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, May 04 2017
STATUS
approved