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A185868
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(Odd,odd)-polka dot array in the natural number array A000027, by antidiagonals.
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5
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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
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refs;
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history;
text;
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OFFSET
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1,2
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COMMENTS
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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
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LINKS
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G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
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FORMULA
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T(n,k) = 2*n-1+(n+k-2)*(2*n+2*k-3).
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EXAMPLE
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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
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MATHEMATICA
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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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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Clark Kimberling, Feb 05 2011
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STATUS
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approved
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