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A078039 Expansion of (1-x)/(1+x-2*x^2+x^3). 15
1, -2, 4, -9, 19, -41, 88, -189, 406, -872, 1873, -4023, 8641, -18560, 39865, -85626, 183916, -395033, 848491, -1822473, 3914488, -8407925, 18059374, -38789712, 83316385, -178955183, 384377665, -825604416, 1773314929, -3808901426, 8181135700, -17572253481, 37743426307, -81069068969 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Comment from Wouter Meeussen, Mar 06 2004: the repeated substitution 0 -> {0,1,2}, 1 -> {0,1,2,3}, 2 -> {0,1}, 3 -> {0,1,2}, starting on list {0} and flattening at each step { {sequence1}, {sequence2},..} to {sequence1,sequence2,..} generates a list after n steps with length =a(n)=A078039.

Sequence is identical to its second differences negated, minus the first 3 terms. - Paul Curtz, Feb 10 2008

LINKS

Table of n, a(n) for n=0..33.

Index entries for linear recurrences with constant coefficients, signature (-1,2,-1).

FORMULA

a(n)= -a(n-1) + 2*a(n-2) - a(n-3). - Paul Curtz, Feb 10 2008

a(n) = (-1)^n * (A002478(n) + A002478(n+1)). - Ralf Stephan, Aug 19 2013

PROG

(PARI) Vec( (1-x)/(1+x-2*x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 23 2012

CROSSREFS

Cf. A002478.

Sequence in context: A141015 A141683 A142474 * A305380 A275862 A036622

Adjacent sequences:  A078036 A078037 A078038 * A078040 A078041 A078042

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified March 24 14:04 EDT 2019. Contains 321448 sequences. (Running on oeis4.)