A220516 Nonnegative integers in square maze arrangement T(n,k), read by antidiagonals, n>=0, k>=0.
0, 1, 3, 8, 2, 4, 9, 7, 5, 15, 24, 10, 6, 14, 16, 25, 23, 11, 13, 17, 35, 48, 26, 22, 12, 18, 34, 36, 49, 47, 27, 21, 19, 33, 37, 63, 80, 50, 46, 28, 20, 32, 38, 62, 64, 81, 79, 51, 45, 29, 31, 39, 61, 65, 99, 120, 82, 78, 52, 44, 30, 40, 60, 66, 98, 100
Offset: 0
Examples
The first layer is [1, 2, 3] which looks like this: . 3, 1, 2, The second layer is [4, 5, 6, 7, 8] which looks like this: . . 4 . . 5, 8, 7, 6, Square array T(0,0)..T(10,10) begins: 0, 3, 4, 15, 16, 35, 36, 63, 64, 99, 100,... 1, 2, 5, 14, 17, 34, 37, 62, 65, 98, 101,... 8, 7, 6, 13, 18, 33, 38, 61, 66, 97, 102,... 9, 10, 11, 12, 19, 32, 39, 60, 67, 96, 103,... 24, 23, 22, 21, 20, 31, 40, 59, 68, 95, 104,... 25, 26, 27, 28, 29, 30, 41, 58, 69, 94, 105,... 48, 47, 46, 45, 44, 43, 42, 57, 70, 93, 106,... 49, 50, 51, 52, 53, 54, 55, 56, 71, 92, 107,... 80, 79, 78, 77, 76, 75, 74, 73, 72, 91, 108,... 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 109,... 120, 119, 118, 117, 116, 115, 114, 113, 112, 111, 110,... ...
Formula
a(n) = A081344(n+1) - 1.
T(n,k) = n^2 + k , if n is odd and k<=n.
T(n,k) = n(n + 2) - k, if n is even and k<=n.
T(n,k) = k(k + 2) - n, if n is odd and n
T(n,k) = k^2 + n , if n is even and n
Comments