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

%I A209634 #19 Sep 29 2013 07:17:29
%S A209634 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,
%T A209634 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,
%U A209634 22,16,10,4,43,37,31,25,19,13,7,1,46,40,34,28,22,16,10
%N A209634 Triangle with (1,4,7,10,13,16...,(3*n-2),...) in every column, shifted down twice.
%C A209634 OEIS contains a lot of similar sequences, for example A152204, A122196, A173284.
%C A209634 Row sums for this sequence gives A006578.
%C A209634 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.
%C A209634 No triangle with primes in every column, shifted down by K>=2 in OEIS, no row sums of it in OEIS.
%C A209634 From _Johannes W. Meijer_, Sep 28 2013: (Start)
%C A209634 Triangle read by rows formed from antidiagonals of triangle A143971.
%C A209634 The alternating row sums equal A004524(n+2) + 2*A004524(n+1).
%C A209634 The antidiagonal sums equal A171452(n+1). (End)
%F A209634 From _Johannes W. Meijer_, Sep 28 2013: (Start)
%F A209634 T(n, k) = 3*n - 6*k + 4, n >= 1 and 1 <= k <= floor((n+1)/2).
%F A209634 T(n, k) = A143971(n-k+1, k), n >= 1 and 1 <= k <= floor((n+1)/2). (End)
%e A209634 Triangle:
%e A209634 1
%e A209634 4
%e A209634 7,  1
%e A209634 10, 4
%e A209634 13, 7,  1
%e A209634 16, 10, 4
%e A209634 19, 13, 7,  1
%e A209634 22, 16, 10, 4
%e A209634 25, 19, 13, 7,  1
%e A209634 28, 22, 16, 10, 4
%e A209634 ...
%p A209634 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
%Y A209634 Cf. A008315, A011973, A102541, A122196, A122197, A128099, A152198, A152204, A173284, A207538.
%Y A209634 Cf. (Related to triangle sums) A006578, A000217, A002620, A004524, A171452.
%K A209634 nonn,easy,tabf
%O A209634 1,2
%A A209634 _Ctibor O. Zizka_, Mar 11 2012