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A158983 Coefficients of polynomials (in descending powers of x) P(n,x) := 2 + P(n-1,x)^2, where P(1,x) = x + 2. 6
1, 2, 1, 4, 6, 1, 8, 28, 48, 38, 1, 16, 120, 544, 1628, 3296, 4432, 3648, 1446, 1, 32, 496, 4928, 35064, 189248, 800992, 2711424, 7419740, 16475584, 29610272, 42666880, 48398416, 41867904, 26125248, 10550016, 2090918, 1, 64, 2016, 41600, 631536 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Clark Kimberling, Polynomials defined by a second-order recurrence, interlacing zeros, and Gray codes, The Fibonacci Quarterly 48 (2010) 209-218.
FORMULA
From Peter Bala, Jul 01 2015: (Start)
P(n,x) = P(n,-4 - x) for n >= 2.
P(n+1,x)= P(n,(2 + x)^2). Thus if alpha is a zero of P(n,x) then sqrt(alpha) - 2 is a zero of P(n+1,x).
Define a sequence of polynomials Q(n,x) by setting Q(1,x) = 2 + x^2 and Q(n,x) = Q(n-1, 2 + x^2) for n >= 2. Then P(n,x) = Q(n,sqrt(x)).
Q(n,x) = Q(k,Q(n-k,x)) for 1 <= k <= n-1; P(n,x) = P(k,P(n-k,x)^2) for 1 <= k <= n - 1.
n-th row sum = P(n,1) = A102847(n);
P(n,1) = P(n+1,-1) = P(n+1,-3); P(n,1) = P(n,-5) for n >= 2.
(End)
EXAMPLE
Row 1: 1 2 (from x+2)
Row 2: 1 4 6 (from x^2+4x+6)
Row 3: 1 8 28 48 38
Row 4: 1 16 120 544 1628 3296 4432 3648 1446
CROSSREFS
Cf. A158982, A158984, A158985, A158986. A102847 (row sums).
Sequence in context: A294440 A346905 A075497 * A261642 A185947 A268472
KEYWORD
nonn,tabf
AUTHOR
Clark Kimberling, Apr 02 2009
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)