A185868 (Odd,odd)-polka dot array in the natural number array A000027, by antidiagonals.

1, 4, 6, 11, 13, 15, 22, 24, 26, 28, 37, 39, 41, 43, 45, 56, 58, 60, 62, 64, 66, 79, 81, 83, 85, 87, 89, 91, 106, 108, 110, 112, 114, 116, 118, 120, 137, 139, 141, 143, 145, 147, 149, 151, 153, 172, 174, 176, 178, 180, 182, 184, 186, 188, 190, 211, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 254, 256, 258, 260, 262, 264, 266, 268, 270, 272, 274, 276, 301, 303, 305, 307, 309, 311, 313, 315, 317, 319, 321, 323, 325, 352, 354, 356, 358, 360, 362, 364, 366, 368, 370, 372, 374, 376, 378

Offset

1,2

Comments

This is one of four polka dot arrays in the natural number array A000027:

(odd,odd): A185868

(odd,even): A185869

(even,odd): A185870

(even,even): A185871

row 1: A084849

col 1: A000384

col 2: A091823

diag (1,13,...): A102083

diag (4,24,...): A085250

antidiagonal sums: A059722

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

T(n,k) = 2*n-1+(n+k-2)*(2*n+2*k-3).

Example

The natural number array A000027 has northwest corner
1...2...4...7...11
3...5...8...12..17
6...9...13..18..24
10..14..19..25..32
15..20..26..33..41
The numbers in (odd,odd) positions comprise A185868:
1....4....11...22...37
6....13...24...39...58
15...26...41...60...83
28...43...62...85...112

Mathematica

f[n_, k_]:=2n-1+(n+k-2)(2n+2k-3);
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

Crossrefs

Cf. A000027 (as an array), A185872, A185869, A185870, A185871.

Sequence in context: A180713 A126591 A031452 * A250125 A190489 A094226

Adjacent sequences: A185865 A185866 A185867 * A185869 A185870 A185871

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 05 2011

Status

approved