1,2

Row sums = the hexagonal numbers, A000384: (1, 6, 15, 28, 45, ...).

From Boris Putievskiy, Jan 24 2013: (Start)

Table T(n,k) = n + 3*k - 3, n, k > 0, read by antidiagonals. General case A209304. Let m be a positive integer. The first column of the table T(n,1) is the sequence of the positive integers A000027. Every subsequent column is formed from the previous column, shifted by m elements.

For m=0 the result is A002260,

for m=1 the result is A002024,

for m=2 the result is A128076,

for m=3 the result is A131914,

for m=4 the result is A209304. (End)

Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012.

3*A002024 - 2*A051340 as infinite lower triangular matrices.

From Boris Putievskiy, Jan 24 2013: (Start)

For the general case

a(n) = m*A003056 - (m-1)*A002260.

a(n) = m*(t+1) + (m-1)*(t*(t+1)/2-n), where t = floor((-1+sqrt(8*n-7))/2).

For m = 3,

a(n) = 3*A003056 - 2*A002260.

a(n) = 3*(t+1) + 2*(t*(t+1)/2-n), where t = floor((-1+sqrt(8*n-7))/2). (End)

First few rows of the triangle:

1;

4, 2;

7, 5, 3;

10, 8, 6, 4;

13, 11, 9, 7, 5;

16, 14, 12, 10, 8, 6;

19, 17, 15, 13, 11, 9, 7;

...

Cf. A002024, A051340, A000384, A003056, A002260, A002024, A128076, A209304.

Sequence in context: A130849 A138754 A021963 * A115302 A109857 A194075

Adjacent sequences: A131911 A131912 A131913 * A131915 A131916 A131917

nonn,tabl

Gary W. Adamson, Jul 27 2007

approved