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
Examples
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
Links
Crossrefs
Transpose: A286156.
Programs
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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 *) -
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
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Scheme
(define (A286157 n) (A286156bi (A004736 n) (A002260 n))) ;; For A286156bi see A286156.
Formula
A(n,k) = A286156(k,n).
Comments