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Number of terms in n-th row of irregular triangle defined in A093911.
1

%I #17 Dec 15 2016 10:41:55

%S 1,2,3,4,6,10,20,40,80,160,308,628,1256,2488,5000,9940,19928,39864,

%T 79660,159380,318724,637496,1274980,2549924,5099884,10199748,20399528,

%U 40799020,81598052,163196124,326392240,652784444,1305568896,2611137796

%N Number of terms in n-th row of irregular triangle defined in A093911.

%C First differences of A093911.

%e From _Michael De Vlieger_, Dec 15 2016: (Start)

%e a(4) = 4 because a(1) is the product of 1 successive numbers starting with 1 = 1, a(2) is the product of 2 successive numbers (2,3) = 6, a(3) is the product of 3 successive numbers (4,5,6) = 120. Finally, a(4) is the product of 4 successive numbers (7,8,9,10) = 5040. All the products have the property that a(n) = 0 (mod a(n - 1)). Thus a(4) = 4. (End)

%t a = {{1, 1}, {2, 2}}; Do[k = Last@ a[[i]]; While[! Divisible[Pochhammer[Total@ a[[i]], k], Pochhammer @@ a[[i]]], k++]; AppendTo[a, {Total@ a[[i]], k}], {i, 2, 16}]; Last /@ a (* _Michael De Vlieger_, Dec 15 2016 *)

%Y Cf. A090906, A093911.

%K nonn,easy,less

%O 1,2

%A _Amarnath Murthy_, Apr 24 2004

%E Edited and extended by _David Wasserman_, Mar 27 2006