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

1,2

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)

Links

Table of n, a(n) for n=1..71.

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)

Example

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
...

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

Crossrefs

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

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

Sequence in context: A093436 A343805 A082169 * A340584 A289523 A078220

Adjacent sequences: A209631 A209632 A209633 * A209635 A209636 A209637

Keyword

nonn,easy,tabf

Author

Ctibor O. Zizka, Mar 11 2012

Status

approved