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A083487 Triangle read by rows: T(n,k) = 2*n*k + n + k (1 <= k <= n).

%I A083487 #46 Oct 17 2023 05:09:45
%S A083487 4,7,12,10,17,24,13,22,31,40,16,27,38,49,60,19,32,45,58,71,84,22,37,
%T A083487 52,67,82,97,112,25,42,59,76,93,110,127,144,28,47,66,85,104,123,142,
%U A083487 161,180,31,52,73,94,115,136,157,178,199,220,34,57,80,103,126,149,172,195,218,241,264
%N A083487 Triangle read by rows: T(n,k) = 2*n*k + n + k (1 <= k <= n).
%C A083487 T(n,k) gives number of edges (of unit length) in a k X n grid.
%C A083487 The values 2*T(n,k)+1 = (2*n+1)*(2*k+1) are nonprime and therefore in A047845.
%H A083487 Vincenzo Librandi, <a href="/A083487/b083487.txt">Rows n = 1..100, flattened</a>
%H A083487 Alain Kraus, <a href="https://www.di.ens.fr/~nitulesc/files/2M220/Cours.pdf">Cours-Arithmétique et algèbre</a>, 2016-2017, Université de Paris VI. See Exercice 6 p. 13.
%H A083487 OEIS Wiki, <a href="/wiki/Odd_composites">Odd composites</a>
%F A083487 From _G. C. Greubel_, Oct 17 2023: (Start)
%F A083487 T(n, 1) = A016777(n).
%F A083487 T(n, 2) = A016873(n).
%F A083487 T(n, 3) = A017017(n).
%F A083487 T(n, 4) = A017209(n).
%F A083487 T(n, 5) = A017449(n).
%F A083487 T(n, 6) = A186113(n).
%F A083487 T(n, n-1) = A056220(n).
%F A083487 T(n, n-2) = A090288(n-2).
%F A083487 T(n, n-3) = A271625(n-2).
%F A083487 T(n, n) = 4*A000217(n).
%F A083487 T(2*n, n) = A033954(n).
%F A083487 Sum_{k=1..n} T(n, k) = A162254(n).
%F A083487 Sum_{k=1..n} (-1)^(k-1)*T(n, k) = A182868((n+1)/2) if n is odd otherwise A182868(n/2) + 1. (End)
%e A083487 Triangle begins:
%e A083487    4;
%e A083487    7, 12;
%e A083487   10, 17, 24;
%e A083487   13, 22, 31, 40;
%e A083487   16, 27, 38, 49,  60;
%e A083487   19, 32, 45, 58,  71,  84;
%e A083487   22, 37, 52, 67,  82,  97, 112;
%e A083487   25, 42, 59, 76,  93, 110, 127, 144;
%e A083487   28, 47, 66, 85, 104, 123, 142, 161, 180;
%t A083487 T[n_,k_]:= 2 n k + n + k; Table[T[n, k], {n, 10}, {k, n}]//Flatten (* _Vincenzo Librandi_, Jun 01 2014 *)
%o A083487 (Magma) [(2*n*k + n + k): k in [1..n], n in [1..11]]; // _Vincenzo Librandi_, Jun 01 2014
%o A083487 (Python)
%o A083487 def T(r, c): return 2*r*c + r + c
%o A083487 a = [T(r, c) for r in range(12) for c in range(1, r+1)]
%o A083487 print(a) # _Michael S. Branicky_, Sep 07 2022
%o A083487 (SageMath) flatten([[2*n*k +n +k for k in range(1,n+1)] for n in range(1,14)]) # _G. C. Greubel_, Oct 17 2023
%Y A083487 Cf. A000217, A016777, A016873, A017017, A017209, A017449, A033954.
%Y A083487 Cf. A056220, A082652, A083003, A090288, A182868, A186113, A271625.
%Y A083487 See A151890 for another version.
%K A083487 nonn,tabl
%O A083487 1,1
%A A083487 Artemario Tadeu Medeiros da Silva (artemario(AT)uol.com.br), Jun 09 2003
%E A083487 Edited by _N. J. A. Sloane_, Jul 23 2009
%E A083487 Name edited by _Michael S. Branicky_, Sep 07 2022