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A185869 (Odd,even)-polka dot array in the natural number array A000027; read by antidiagonals. 5
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)