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%I #5 Aug 29 2013 14:26:56
%S 1,3,4,7,10,14,13,20,30,44,21,34,54,84,128,31,52,86,140,224,352,43,74,
%T 126,212,352,576,928,57,100,174,300,512,864,1440,2368,73,130,230,404,
%U 704,1216,2080,3520,5888,91,164,294,524,928,1632,2848,4928,8448
%N Triangle read by rows: T(n,1) = n * (n - 1) + 1 and for k: 1 < k <= n: T(n,k) = T(n,k-1) + T(n-1,k-1).
%C T(n,1) = A002061(n); T(n,2) = A005893(n-1) for n > 1;
%C T(n,n) = A007466(n).
%H Reinhard Zumkeller, <a href="/A228643/b228643.txt">Rows n = 1..100 of table, flattened</a>
%e . 1: 1
%e . 2: 3, 4
%e . 3: 7, 10, 14
%e . 4: 13, 20, 30, 44
%e . 5: 21, 34, 54, 84, 128
%e . 6: 31, 52, 86,140, 224, 352
%e . 7: 43, 74,126,212, 352, 576, 928
%e . 8: 57,100,174,300, 512, 864,1440,2368
%e . 9: 73,130,230,404, 704,1216,2080,3520, 5888
%e . 10: 91,164,294,524, 928,1632,2848,4928, 8448,14336
%e . 11: 111,202,366,660,1184,2112,3744,6592,11520,19968,34304
%e . 12: 133,244,446,812,1472,2656,4768,8512,15104,26624,46592,80896.
%o (Haskell)
%o a228643 n k = a228643_tabl !! (n-1) !! (k-1)
%o a228643_row n = a228643_tabl !! (n-1)
%o a228643_tabl = map fst $ iterate
%o (\(row, x) -> (scanl (+) (x * (x - 1) + 1) row, x + 1)) ([1], 2)
%K nonn,tabl
%O 1,2
%A _J. M. Bergot_ and _Reinhard Zumkeller_, Aug 29 2013
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