A209634 Triangle with (1,4,7,10,13,16...,(3*n-2),...) in every column, shifted down twice.

1, 4, 7, 1, 10, 4, 13, 7, 1, 16, 10, 4, 19, 13, 7, 1, 22, 16, 10, 4, 25, 19, 13, 7, 1, 28, 22, 16, 10, 4, 31, 25, 19, 13, 7, 1, 34, 28, 22, 16, 10, 4, 37, 31, 25, 19, 13, 7, 1, 40, 34, 28, 22, 16, 10, 4, 43, 37, 31, 25, 19, 13, 7, 1, 46, 40, 34, 28, 22, 16, 10

Offset: 1

Author

Ctibor O. Zizka, Mar 11 2012

Keywords

• nonn
• easy
• tabf

Comments

OEIS contains a lot of similar sequences, for example A152204, A122196, A173284.

Row sums for this sequence gives A006578.

In general, by given triangle with (A-B,2*A-B,...,A*n-B,...) in every column, shifted down K-times, we have the row sum s(n)= A*(n*n+K*n+nmodK)/(2*K) - B*(n+nmodK)/K. In this sequence K=2,A=3,B=2, in A152204 K=2,A=2,B=1.

No triangle with primes in every column, shifted down by K>=2 in OEIS, no row sums of it in OEIS.

From Johannes W. Meijer, Sep 28 2013: (Start)

Triangle read by rows formed from antidiagonals of triangle A143971.

The alternating row sums equal A004524(n+2) + 2*A004524(n+1).

The antidiagonal sums equal A171452(n+1). (End)

Examples

			Triangle:
1
4
7,  1
10, 4
13, 7,  1
16, 10, 4
19, 13, 7,  1
22, 16, 10, 4
25, 19, 13, 7,  1
28, 22, 16, 10, 4
...
		

Crossrefs

Cf. A008315, A011973, A102541, A122196, A122197, A128099, A152198, A152204, A173284, A207538.

Cf. (Related to triangle sums) A006578, A000217, A002620, A004524, A171452.

Programs

Maple

T := (n, k) -> 3*n - 6*k + 4: seq(seq(T(n, k), k=1..floor((n+1)/2)), n=1..15); # Johannes W. Meijer, Sep 28 2013

Formula

From Johannes W. Meijer, Sep 28 2013: (Start)

T(n, k) = 3*n - 6*k + 4, n >= 1 and 1 <= k <= floor((n+1)/2).

T(n, k) = A143971(n-k+1, k), n >= 1 and 1 <= k <= floor((n+1)/2). (End)