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A185868 (Odd,odd)-polka dot array in the natural number array A000027, by antidiagonals. 5

%I #11 Jul 15 2017 02:13:36

%S 1,4,6,11,13,15,22,24,26,28,37,39,41,43,45,56,58,60,62,64,66,79,81,83,

%T 85,87,89,91,106,108,110,112,114,116,118,120,137,139,141,143,145,147,

%U 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

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

%C This is one of four polka dot arrays in the natural number array A000027:

%C (odd,odd): A185868

%C (odd,even): A185869

%C (even,odd): A185870

%C (even,even): A185871

%C row 1: A084849

%C col 1: A000384

%C col 2: A091823

%C diag (1,13,...): A102083

%C diag (4,24,...): A085250

%C antidiagonal sums: A059722

%H G. C. Greubel, <a href="/A185868/b185868.txt">Table of n, a(n) for the first 50 rows, flattened</a>

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

%e The natural number array A000027 has northwest corner

%e 1...2...4...7...11

%e 3...5...8...12..17

%e 6...9...13..18..24

%e 10..14..19..25..32

%e 15..20..26..33..41

%e The numbers in (odd,odd) positions comprise A185868:

%e 1....4....11...22...37

%e 6....13...24...39...58

%e 15...26...41...60...83

%e 28...43...62...85...112

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

%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), A185872, A185869, A185870, A185871.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Feb 05 2011

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