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A106393 Expansion of 1/(1 - 8x + 17x^2). 0
1, 8, 47, 240, 1121, 4888, 20047, 77280, 277441, 905768, 2529647, 4839120, -4291039, -116593352, -859799153, -4896306240, -24553864319, -113193708472, -488133974353, -1980778750800, -7547952442399, -26710380775592, -85367854683953, -228866364286560, -379677384665279 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

In general, the sequence with g.f. 1/(1-2r*x+(r^2+1)*x^2)=1/((1-r*x)^2+x^2) has a(n)=sum{k=0..floor(n/2), binomial(n-k,k)(r^2-1)^k*(2r)^(n-2k)}; a(n)=sum{k=0..floor((n+1)/2), binomial(n+1,2k+1)(-1)^k*r^(n-2k)}.

LINKS

Table of n, a(n) for n=0..24.

Index entries for linear recurrences with constant coefficients, signature (8,-17)

FORMULA

G.f.: 1/((1-4*x)^2+x^2);

a(n) = sum{k=0..floor(n/2), binomial(n-k, k)(-17)^k*8^(n-2k)};

a(n) = sum{k=0..floor((n+1)/2), binomial(n+1, 2k+1)(-1)^k*4^(n-2k)}.

a(n) = 8*a(n-1) -17*a(n-2), n >= 2. - Vincenzo Librandi, Mar 18 2011

MATHEMATICA

Join[{a=1, b=8}, Table[c=8*b-17*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 20 2011 *)

PROG

(Sage) [lucas_number1(n, 8, 17) for n in xrange(1, 26)] # Zerinvary Lajos, Apr 23 2009

CROSSREFS

Sequence in context: A296331 A081279 A099110 * A300167 A029760 A139262

Adjacent sequences:  A106390 A106391 A106392 * A106394 A106395 A106396

KEYWORD

easy,sign

AUTHOR

Paul Barry, May 01 2005

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)