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A084608 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1+2x+3x^2)^n. 5
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; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Rows n = 0..100, flattened

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,

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

MATHEMATICA

row[n_] := (1+2x+3x^2)^n + O[x]^(2n+1) // CoefficientList[#, x]&; Table[row[n], {n, 0, 10}] // Flatten (* Jean-Fran├žois Alcover, Feb 01 2017 *)

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

CROSSREFS

Cf. A002426, A084600-A084606, A006139, A084609-A084615.

Sequence in context: A076732 A130152 A211233 * A078990 A176566 A079639

Adjacent sequences:  A084605 A084606 A084607 * A084609 A084610 A084611

KEYWORD

nonn,tabf

AUTHOR

Paul D. Hanna, Jun 01 2003

STATUS

approved

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Last modified August 20 23:38 EDT 2019. Contains 326155 sequences. (Running on oeis4.)