A257258 Square array A(row,col) = (1/2) * (A255127(row,col+1) - A255127(row,col)): half of the first differences of each row of Ludic array.

1, 1, 3, 1, 3, 7, 1, 3, 8, 12, 1, 3, 7, 14, 22, 1, 3, 8, 13, 24, 30, 1, 3, 7, 14, 24, 30, 42, 1, 3, 8, 12, 26, 32, 43, 61, 1, 3, 7, 13, 24, 33, 47, 63, 71, 1, 3, 8, 14, 24, 31, 43, 66, 72, 88, 1, 3, 7, 13, 22, 30, 47, 60, 73, 83, 108, 1, 3, 8, 12, 24, 32, 43, 66, 71, 90, 117, 126

Offset

1,3

Comments

The array A(row,col) is read by downwards antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of the array

Formula

A(row,col) = (1/2) * (A255127(row,col+1) - A255127(row,col)).

A(row,col) = A257257(row,col)/2.

Example

The top left corner of the array:
    1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1,   1
    3,   3,   3,   3,   3,   3,   3,   3,   3,   3,   3,   3,   3,   3,   3,   3
    7,   8,   7,   8,   7,   8,   7,   8,   7,   8,   7,   8,   7,   8,   7,   8
   12,  14,  13,  14,  12,  13,  14,  13,  12,  14,  13,  14,  12,  13,  14,  13
   22,  24,  24,  26,  24,  24,  22,  24,  26,  24,  24,  24,  22,  26,  24,  24
   30,  30,  32,  33,  31,  30,  32,  31,  30,  35,  30,  30,  31,  32,  30,  33
   42,  43,  47,  43,  47,  43,  41,  46,  44,  46,  44,  45,  45,  42,  45,  45
   61,  63,  66,  60,  66,  63,  65,  63,  60,  66,  64,  63,  65,  64,  63,  65
   71,  72,  73,  71,  73,  69,  75,  74,  70,  74,  73,  69,  75,  69,  75,  74
   88,  83,  90,  84,  88,  89,  85,  89,  85,  90,  87,  86,  88,  89,  88,  87
  108, 117, 113, 121, 114, 113, 120, 109, 117, 123, 110, 115, 117, 113, 117, 118
  126, 135, 127, 137, 129, 127, 129, 138, 131, 133, 129, 128, 132, 138, 132, 132
  137, 142, 134, 142, 152, 135, 141, 139, 147, 141, 141, 138, 141, 144, 146, 138
  154, 158, 157, 158, 160, 158, 156, 154, 162, 168, 158, 151, 158, 157, 161, 157
  180, 180, 177, 184, 180, 186, 185, 184, 176, 180, 190, 177, 185, 190, 176, 184
  206, 217, 212, 210, 213, 220, 213, 210, 216, 212, 211, 222, 212, 211, 215, 213
  ...

Prog

(Scheme)
(define (A257258 n) (A257258bi (A002260 n) (A004736 n)))
(define (A257258bi row col) (* (/ 1 2) (- (A255127bi row (+ 1 col)) (A255127bi row col)))) ;; Code for A255127bi given in A255127.

Crossrefs

Column 1: A256483.

Cf. A255127, A257257 (same array but with terms multiplied by 2).

Sequence in context: A152903 A226522 A122507 * A259325 A094250 A208517

Adjacent sequences: A257255 A257256 A257257 * A257259 A257260 A257261

Keyword

nonn,tabl

Author

Antti Karttunen, Apr 29 2015

Status

approved