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 A182579 Triangle read by rows: T(0,0) = 1, for n>0: T(n,n) = 2 and for k<=floor(n/2): T(n,2*k) = n/(n-k) * binomial(n-k,k), T(n,2*k+1) = (n-1)/(n-1-k) * binomial(n-1-k,k). 8
 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 1, 5, 4, 5, 2, 1, 1, 6, 5, 9, 5, 2, 1, 1, 7, 6, 14, 9, 7, 2, 1, 1, 8, 7, 20, 14, 16, 7, 2, 1, 1, 9, 8, 27, 20, 30, 16, 9, 2, 1, 1, 10, 9, 35, 27, 50, 30, 25, 9, 2, 1, 1, 11, 10, 44, 35, 77, 50, 55, 25, 11, 2 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A000204(n+1) = sum of n-th row, Lucas numbers; A000204(n+3) = alternating row sum of n-th row; A182584(n) = T(2*n,n), central terms; A000012(n) = T(n,0), left edge; A040000(n) = T(n,n), right edge; A054977(n-1) = T(n,1) for n > 0; A109613(n-1) = T(n,n-1) for n > 0; A008794(n) = T(n,n-2) for n > 1. LINKS Reinhard Zumkeller, Rows n = 0..150 of triangle, flattened Henry W. Gould, A Variant of Pascal's Triangle, The Fibonacci Quarterly, Vol. 3, Nr. 4, Dec. 1965, p. 261ff. FORMULA T(n+1,2*k+1) = T(n,2*k), T(n+1,2*k) = T(n,2*k-1) + T(n,2*k). EXAMPLE Starting with 2nd row = [1 2] the rows of the triangle are defined recursively without computing explicitely binomial coefficients; demonstrated for row 8, (see also Haskell program): .  (0) 1  1  7  6 14  9  7  2      [A]  row 7 prepended by 0 .   1  1  7  6 14  9  7  2 (0)     [B]  row 7, 0 appended .   1  0  1  0  1  0  1  0  1      [C]  1 and 0 alternating .   1  0  7  0 14  0  7  0  0      [D]  = [B] multiplied by [C] .   1  1  8  7 20 14 16  7  2      [E]  = [D] added to [A] = row 8. The triangle begins:                 | A000204 .             1                      |       1 .            1  2                    |       3 .           1  1  2                  |       4 .          1  1  3  2                |       7 .         1  1  4  3  2              |      11 .        1  1  5  4  5  2            |      18 .       1  1  6  5  9  5  2          |      29 .      1  1  7  6 14  9  7  2        |      47 .     1  1  8  7 20 14 16  7  2      |      76 .    1  1  9  8 27 20 30 16  9  2    |     123 .   1  1 10  9 35 27 50 30 25  9  2  |     199 . PROG (Haskell) a182579 n k = a182579_tabl !! n !! k a182579_row n = a182579_tabl !! n a182579_tabl = [1] : iterate (\row ->   zipWith (+) ([0] ++ row) (zipWith (*) (row ++ [0]) a059841_list)) [1, 2] CROSSREFS Cf. A065941, A059841. Sequence in context: A108316 A322426 A145574 * A290737 A056138 A067594 Adjacent sequences:  A182576 A182577 A182578 * A182580 A182581 A182582 KEYWORD nonn,tabl AUTHOR Reinhard Zumkeller, May 06 2012 STATUS approved

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Last modified September 18 20:22 EDT 2019. Contains 327181 sequences. (Running on oeis4.)