A134483 - OEIS

%I #23 Oct 14 2022 12:01:56

%S 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 18,19,15,16,17,18,19,20,21,22,17,18,19,20,21,22,23,24,25,19,20,21,22,

%U 23,24,25,26,27,28

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

%C Row sums are the heptagonal numbers, A000566: (1, 7, 18, 34, 55, 81, ...).

%C Row n consists of n consecutive integers starting with 2n-1. - _Emeric Deutsch_, Nov 04 2007

%H Boris Putievskiy, <a href="/A134483/b134483.txt">Rows n = 1..140 of triangle, flattened</a>

%H 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 From _Emeric Deutsch_, Nov 04 2007: (Start)

%F T(n,k) = 2n + k - 2 for 1 <= k <= n.

%F G.f. = t*z(1 + z + 2*t*z - 4*t*z^2)/((1-z)^2*(1-t*z)^2). (End)

%F From _Boris Putievskiy_, Jan 16 2013: (Start)

%F a(n) = A002260(n) + 2*A003056(n);

%F a(n) = j+2*t, where j = n - t*(t+1)/2, t = floor((-1+sqrt(8*n-7))/2). (End)

%e First few rows of the triangle:

%e   1;

%e   3,  4;

%e   5,  6,  7;

%e   7,  8,  9, 10;

%e   9, 10, 11, 12, 13;

%e   ...

%p 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 Table[2n+k-2,{n,10},{k,n}]//Flatten (* _Harvey P. Dale_, Oct 14 2022 *)

%Y Cf. A000566.

%Y Cf. A002260, A003056.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, Oct 27 2007