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A134483 Triangle read by rows: T(n,k) = 2n + k - 2; 1 <= k <= n.

%I A134483 #23 Oct 14 2022 12:01:56
%S A134483 1,3,4,5,6,7,7,8,9,10,9,10,11,12,13,11,12,13,14,15,16,13,14,15,16,17,
%T A134483 18,19,15,16,17,18,19,20,21,22,17,18,19,20,21,22,23,24,25,19,20,21,22,
%U A134483 23,24,25,26,27,28
%N A134483 Triangle read by rows: T(n,k) = 2n + k - 2; 1 <= k <= n.
%C A134483 Row sums are the heptagonal numbers, A000566: (1, 7, 18, 34, 55, 81, ...).
%C A134483 Row n consists of n consecutive integers starting with 2n-1. - _Emeric Deutsch_, Nov 04 2007
%H A134483 Boris Putievskiy, <a href="/A134483/b134483.txt">Rows n = 1..140 of triangle, flattened</a>
%H A134483 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations [of] Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%F A134483 From _Emeric Deutsch_, Nov 04 2007: (Start)
%F A134483 T(n,k) = 2n + k - 2 for 1 <= k <= n.
%F A134483 G.f. = t*z(1 + z + 2*t*z - 4*t*z^2)/((1-z)^2*(1-t*z)^2). (End)
%F A134483 From _Boris Putievskiy_, Jan 16 2013: (Start)
%F A134483 a(n) = A002260(n) + 2*A003056(n);
%F A134483 a(n) = j+2*t, where j = n - t*(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). (End)
%e A134483 First few rows of the triangle:
%e A134483   1;
%e A134483   3,  4;
%e A134483   5,  6,  7;
%e A134483   7,  8,  9, 10;
%e A134483   9, 10, 11, 12, 13;
%e A134483   ...
%p A134483 for n to 10 do seq(2*n+k-2,k=1..n) end do; # yields sequence in triangular form - _Emeric Deutsch_, Nov 04 2007
%t A134483 Table[2n+k-2,{n,10},{k,n}]//Flatten (* _Harvey P. Dale_, Oct 14 2022 *)
%Y A134483 Cf. A000566.
%Y A134483 Cf. A002260, A003056.
%K A134483 nonn,tabl
%O A134483 1,2
%A A134483 _Gary W. Adamson_, Oct 27 2007