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 A181971 Triangle read by rows: T(n,0) = 1, T(n,n) = floor((n+3)/2) and T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n. 10
 1, 1, 2, 1, 3, 2, 1, 4, 5, 3, 1, 5, 9, 8, 3, 1, 6, 14, 17, 11, 4, 1, 7, 20, 31, 28, 15, 4, 1, 8, 27, 51, 59, 43, 19, 5, 1, 9, 35, 78, 110, 102, 62, 24, 5, 1, 10, 44, 113, 188, 212, 164, 86, 29, 6, 1, 11, 54, 157, 301, 400, 376, 250, 115, 35, 6, 1, 12, 65 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Another variant of Pascal's triangle; row sums: A081254; central terms: T(2*n,n) = A128082(n+1); T(n,0) = 1; T(n,1) = n + 1 for n > 0; T(n,2) = A000096(n-1) for n > 1; T(n,3) = A105163(n-2) for n > 2; T(n,n-2) = A005744(n-1) for n > 1; T(n,n-1) = A024206(n) for n > 0; T(n,n) = A008619(n+1). LINKS Reinhard Zumkeller, Rows n=0..150 of triangle, flattened EXAMPLE The triangle begins: .  0:                              1 .  1:                           1     2 .  2:                        1     3     2 .  3:                     1     4     5     3 .  4:                  1     5     9     8     3 .  5:               1     6    14    17    11     4 .  6:            1     7    20    31    28    15     4 .  7:         1     8    27    51    59    43    19     5 .  8:      1     9    35    78   110   102    62    24     5 .  9:   1    10    44   113   188   212   164    86    29     6. PROG (Haskell) a181971 n k = a181971_tabl !! n !! k a181971_row n = a181971_tabl !! n a181971_tabl = map snd \$ iterate f (1, [1]) where    f (i, row) = (1 - i, zipWith (+) ([0] ++ row) (row ++ [i])) (PARI) {T(n, k)=if(n==k, (n+3)\2, if(k==0, 1, if(n>k, T(n-1, k-1)+T(n-1, k))))} for(n=0, 12, for(k=0, n, print1(T(n, k), ", ")); print("")) \\ Paul D. Hanna, Jul 18 2012 CROSSREFS Cf. A035317, A007318, A074909. Sequence in context: A293600 A191395 A183917 * A104741 A167237 A277813 Adjacent sequences:  A181968 A181969 A181970 * A181972 A181973 A181974 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, Jul 09 2012 STATUS approved

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Last modified April 17 13:31 EDT 2021. Contains 343063 sequences. (Running on oeis4.)