A185869 (Odd,even)-polka dot array in the natural number array A000027; read by antidiagonals.

2, 7, 9, 16, 18, 20, 29, 31, 33, 35, 46, 48, 50, 52, 54, 67, 69, 71, 73, 75, 77, 92, 94, 96, 98, 100, 102, 104, 121, 123, 125, 127, 129, 131, 133, 135, 154, 156, 158, 160, 162, 164, 166, 168, 170, 191, 193, 195, 197, 199, 201, 203, 205, 207, 209, 232, 234, 236, 238, 240, 242, 244, 246, 248, 250, 252, 277, 279, 281, 283, 285, 287, 289, 291, 293, 295, 297, 299, 326, 328, 330, 332, 334, 336, 338, 340, 342, 344, 346, 348, 350, 379, 381, 383, 385, 387, 389, 391, 393, 395, 397, 399, 401, 403, 405

Offset

1,1

Comments

This is the second of four polka dot arrays; see A185868.

row 1: A130883;

row 2: A100037;

row 3: A100038;

row 4: A100039;

col 1: A014107;

col 2: A033537;

col 3: A100040;

col 4: A100041;

diag (2,18,...): A077591;

diag (7,31,...): A157914;

diag (16,48,...): A035008;

diag (29,69,...): A108928;

antidiagonal sums: A033431;

antidiagonal sums: 2*(1^3, 2^3, 3^3, 4^3,...) = 2*A000578.

A060432(n) + n is odd if and only if n is in this sequence. - Peter Kagey, Feb 03 2016

Links

Peter Kagey, Table of n, a(n) for n = 1..10000

Formula

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

Example

Northwest corner:
2....7....16...29...46
9....18...31...48...69
20...33...50...71...96
35...52...73...98...127

Mathematica

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

Prog

(Haskell)
a185869 n = a185869_list !! (n - 1)
a185869_list = scanl (+) 2 $ a' 1
  where  a' n = 2 * n + 3 : replicate n 2 ++ a' (n + 1)
-- Peter Kagey, Sep 02 2016

Crossrefs

Cf. A000027 (as an array), A060432, A185868, A185870, A185871.

Sequence in context: A106352 A098017 A225675 * A020894 A165995 A287575

Adjacent sequences: A185866 A185867 A185868 * A185870 A185871 A185872

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 05 2011

Status

approved