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A285723 Transpose of square array A285722. 3
0, 1, 1, 3, 0, 2, 6, 2, 3, 4, 10, 5, 0, 5, 7, 15, 9, 4, 6, 8, 11, 21, 14, 8, 0, 9, 12, 16, 28, 20, 13, 7, 10, 13, 17, 22, 36, 27, 19, 12, 0, 14, 18, 23, 29, 45, 35, 26, 18, 11, 15, 19, 24, 30, 37, 55, 44, 34, 25, 17, 0, 20, 25, 31, 38, 46, 66, 54, 43, 33, 24, 16, 21, 26, 32, 39, 47, 56, 78, 65, 53, 42, 32, 23, 0, 27, 33, 40, 48, 57, 67, 91, 77, 64, 52, 41, 31, 22, 28, 34, 41, 49, 58, 68, 79 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

See A285722.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..7260; the first 120 antidiagonals of the array

FORMULA

A(n,k) = A285722(k,n).

EXAMPLE

The top left 14 X 14 corner of the array:

   0,  1,  3,  6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91

   1,  0,  2,  5,  9, 14, 20, 27, 35, 44, 54, 65, 77, 90

   2,  3,  0,  4,  8, 13, 19, 26, 34, 43, 53, 64, 76, 89

   4,  5,  6,  0,  7, 12, 18, 25, 33, 42, 52, 63, 75, 88

   7,  8,  9, 10,  0, 11, 17, 24, 32, 41, 51, 62, 74, 87

  11, 12, 13, 14, 15,  0, 16, 23, 31, 40, 50, 61, 73, 86

  16, 17, 18, 19, 20, 21,  0, 22, 30, 39, 49, 60, 72, 85

  22, 23, 24, 25, 26, 27, 28,  0, 29, 38, 48, 59, 71, 84

  29, 30, 31, 32, 33, 34, 35, 36,  0, 37, 47, 58, 70, 83

  37, 38, 39, 40, 41, 42, 43, 44, 45,  0, 46, 57, 69, 82

  46, 47, 48, 49, 50, 51, 52, 53, 54, 55,  0, 56, 68, 81

  56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66,  0, 67, 80

  67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78,  0, 79

  79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91,  0

MATHEMATICA

A[n_, n_] = 0;

A[n_, k_] /; k == n - 1 := (k^2 - k + 2)/2;

A[1, k_] := (k^2 - 3 k + 4)/2;

A[n_, k_] /; 1 <= k <= n - 2 := A[n, k] = A[n, k + 1] + 1;

A[n_, k_] /; k > n := A[n, k] = A[n - 1, k] + 1;

T[n_, k_] := A[k, n];

Table[T[n - k + 1, k], {n, 1, 14}, {k, n, 1, -1}] // Flatten (* Jean-Fran├žois Alcover, Nov 19 2019 *)

PROG

(Scheme) (define (A285723 n) (A285722bi (A004736 n) (A002260 n))) ;; For A285722bi see A285722.

(Python)

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

def A(n, k): return 0 if n == k else T(n - k, k) if n>k else T(n, k - n)

for n in range(1, 21): print [A(n - k + 1, k) for k in range(1, n + 1)] # Indranil Ghosh, May 03 2017~

CROSSREFS

Transpose: A285722.

Cf. A000217 (row 1), A000124 (column 1, from 1 onward).

Cf. also A285733.

Sequence in context: A222602 A058544 A112156 * A072328 A135040 A048733

Adjacent sequences:  A285720 A285721 A285722 * A285724 A285725 A285726

KEYWORD

nonn,tabl

AUTHOR

Antti Karttunen, May 03 2017

STATUS

approved

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Last modified September 30 18:12 EDT 2020. Contains 337440 sequences. (Running on oeis4.)