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A100434 G.f.: (1+x)*(3+x)/(1+6*x^2+x^4). 0
3, 4, -17, -24, 99, 140, -577, -816, 3363, 4756, -19601, -27720, 114243, 161564, -665857, -941664, 3880899, 5488420, -22619537, -31988856, 131836323, 186444716, -768398401, -1086679440, 4478554083, 6333631924, -26102926097, -36915112104, 152139002499, 215157040700 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Comments from Creighton Dement, Dec 18 2004: "Define the following sequences:

"b(2n) = c(2n+1), b(2n+1) = c(2n); (c(n)) = (1, -3, -7, 17, 41, -99, -239, 577, 1393, -3363, -8119, 19601, 47321). This is the sequence A001333, apart from signs. Then c(2n) = ((-1)^n)*A002315(n) and c(2n+1) = ((-1)^(n+1))*A001541(n+1).

"(d(n)) = (2, 4, -10, -24, 58, 140, -338, -816, 1970, 4756, -11482, -27720). This is A052542, apart from signs. Also, d(2n) = ((-1)^n)*A075870(n), d(2n+1) = ((-1)^n)*A005319(n+1)

"(e(n)) = (1, -1, -5, 5, 29, -29, -169, 169, 985, -985, -5741, 5741, 33461, -33461), e(2n) = d(2n)/2, e(2n+1) = - d(2n)/2

"(f(n)) = (2, 2, -12, -12, 70, 70, -408, -408, 2378, 2378, -13860, -13860, ) f(2n) = f(2n+1) = d(2n+1)/2

"(g(n)) = (0, -3, 0, 17, 0, -99, 0, 577, 0, -3363, 0, 19601, 0, -114243, 0, 665857), g(2n) = 0, g(2n+1) = c(2n+1)

"Then a(2n) = - c(2n+1), a(2n+1) = d(2n+1) and we have the following conjectures: c(n) + d(n) = e(n) + f(n) = g(n) + a(n); c(n) + d(n) = b(n). In other words, the sequences (c(n) + d(n)) = (e(n) + f(n)) = (g(n) + h(n)) all represent the sequence c with even and odd indexed terms reversed! "

LINKS

Table of n, a(n) for n=0..29.

Index entries for linear recurrences with constant coefficients, signature (0,-6,0,-1).

FORMULA

Conjecture: a(n)=A126354(n+3)*A000034(n)*(-1)^[n/2]. [From R. J. Mathar, Mar 08 2009]

a(n) = -2*a(n-1)-3*a(n-2) if n is even. a(n) = (4*a(n-1)-a(n-2))/3 if n is odd. - R. J. Mathar, Jun 18 2014

CROSSREFS

Bisections give A001541, A005319.

Sequence in context: A082000 A100560 A025534 * A096876 A257330 A115388

Adjacent sequences:  A100431 A100432 A100433 * A100435 A100436 A100437

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 21 2004, suggested by correspondence from Creighton Dement

STATUS

approved

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Last modified May 25 01:01 EDT 2017. Contains 287008 sequences.