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

Author

Antti Karttunen, Apr 29 2015

Keywords

• nonn
• tabl

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), ...

Examples

			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
  ...
		

Links

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

Crossrefs

Column 1: A256483.

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

Programs

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.

Formula

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

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