%I #9 Jul 15 2017 19:11:46

%S 3,8,10,17,19,21,30,32,34,36,47,49,51,53,55,68,70,72,74,76,78,93,95,

%T 97,99,101,103,105,122,124,126,128,130,132,134,136,155,157,159,161,

%U 163,165,167,169,171,192,194,196,198,200,202,204,206,208,210,233,235,237,239,241,243,245,247,249,251,253,278,280,282,284,286,288,290,292,294,296,298,300,327,329,331,333,335,337,339,341,343,345,347,349,351,380,382,384,386,388,390,392,394,396,398,400,402,404,406

%N (Even,odd)-polka dot array in the natural number array A000027, by antidiagonals.

%C This is the third of four polka dot arrays in the array A000027. See A185868.

%C row 1: A033816

%C col 1: A014105

%C col 2: -A168244

%C antidiagonal sums: A061317

%C antidiagonal sums: 3*(octahedral numbers) = 3*A005900.

%H G. C. Greubel, <a href="/A185870/b185870.txt">Table of n, a(n) for the first 50 rows, flattened</a>

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

%e Northwest corner:

%e 3....8....17...30...47

%e 10...19...32...49...70

%e 21...34...51...72...97

%e 36...53...74...99...128

%t f[n_,k_]:=2n+(2n+2k-3)(n+k-1);

%t TableForm[Table[f[n,k],{n,1,10},{k,1,15}]]

%t Table[f[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten

%Y Cf. A000027 (as an array), A185868, A185869, A185871.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Feb 05 2011