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 A209634 Triangle with (1,4,7,10,13,16...,(3*n-2),...) in every column, shifted down twice. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified May 18 19:58 EDT 2021. Contains 344002 sequences. (Running on oeis4.)