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(Even,even)-polka dot array in the natural number array A000027, by antidiagonals.
4

%I #8 Jul 15 2017 19:24:40

%S 5,12,14,23,25,27,38,40,42,44,57,59,61,63,65,80,82,84,86,88,90,107,

%T 109,111,113,115,117,119,138,140,142,144,146,148,150,152,173,175,177,

%U 179,181,183,185,187,189,212,214,216,218,220,222,224,226,228,230,255,257,259,261,263,265,267,269,271,273,275,302,304,306,308,310,312,314,316,318,320,322,324,353,355,357,359,361,363,365,367,369,371,373,375,377,408,410,412,414,416,418,420,422,424,426,428,430,432,434

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

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

%C row 1: A096376

%C col 1: A014106

%C col 2: A071355

%C diag (5,25,...): A080856

%C diag (12,40,...): A033586

%C antidiagonal sums: A048395 (sums of consecutive squares)

%H G. C. Greubel, <a href="/A185871/b185871.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-1), k>=1, n>=1.

%e Northwest corner:

%e 5....12...23...38...57

%e 14...25...40...59...82

%e 27...42...61...84...111

%e 44...63...86...113..144

%t f[n_,k_]:=2n+(n+k-1)(2n+2k-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, A185870.

%K nonn,tabl

%O 1,1

%A _Clark Kimberling_, Feb 05 2011