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A084608
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Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+2x+3x^2)^n.
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4
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1, 1, 2, 3, 1, 4, 10, 12, 9, 1, 6, 21, 44, 63, 54, 27, 1, 8, 36, 104, 214, 312, 324, 216, 81, 1, 10, 55, 200, 530, 1052, 1590, 1800, 1485, 810, 243, 1, 12, 78, 340, 1095, 2712, 5284, 8136, 9855, 9180, 6318, 2916, 729, 1, 14, 105, 532, 2009, 5922, 13993, 26840, 41979
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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EXAMPLE
| Triangle begins:
1,
1, 2, 3,
1, 4, 10, 12, 9,
1, 6, 21, 44, 63, 54, 27,
1, 8, 36, 104, 214, 312, 324, 216, 81,
1, 10, 55, 200, 530, 1052, 1590, 1800, 1485, 810, 243,
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MAPLE
| f:= proc(n) option remember; expand ((1+2*x+3*x^2)^n) end:
T:= (n, k)-> coeff (f(n), x, k):
seq (seq (T(n, k), k=0..2*n), n=0..10); # Alois P. Heinz, Apr 03 2011
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PROG
| (PARI) for(n=0, 10, for(k=0, 2*n, t=polcoeff((1+2*x+3*x^2)^n, k, x); print1(t", ")); print(" "))
(Haskell)
a084608 n = a084608_list !! n
a084608_list = concat $ iterate ([1, 2, 3] *) [1]
instance Num a => Num [a] where
fromInteger k = [fromInteger k]
(p:ps) + (q:qs) = p + q : ps + qs
ps + qs = ps ++ qs
(p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs
_ * _ = []
-- Reinhard Zumkeller, Apr 02 2011
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CROSSREFS
| Cf. A002426, A084600-A084606, A006139, A084609-A084615.
Sequence in context: A193920 A076732 A130152 * A078990 A176566 A079639
Adjacent sequences: A084605 A084606 A084607 * A084609 A084610 A084611
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KEYWORD
| nonn,tabf
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jun 01 2003
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