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A244213 Inverse binomial transform of -2 followed by A000032(n+1). 1
-2, 3, -1, 0, 3, -7, 14, -25, 43, -72, 119, -195, 318, -517, 839, -1360, 2203, -3567, 5774, -9345, 15123, -24472, 39599, -64075, 103678, -167757, 271439, -439200, 710643, -1149847, 1860494, -3010345, 4870843, -7881192 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A simple transform of a(n) is a(n) with -a(0) instead of nonzero a(0) (or -a(0) followed by a(n+1)). Example: -1 followed by A198631(n+1)/A006519(n+2). Its inverse binomial transform is -1, 3/2, -2, 9/4, -2, 3/2, -2,... = -(-1)^n*A143074(n).

Difference table of -2 followed by A000032(n+1):

-2,  1,  3,  4,  7, 11, 18,...

3,   2,  1,  3,  4,  7, 11,...

-1, -1,  2,  1,  3,  4,  7,...

0,   3, -1,  2,  1,  3,  4,...

3,  -4,  3, -1,  2,  1,  3,...

-7,  7, -4,  3, -1,  2,  1,...

14, -11, 7, -4,  3, -1,  2,...

etc.

a(n) is the first column.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (-2,0,1).

FORMULA

a(n) = -2, 3, -1, followed by -(-1)^n*A206417(n).

a(n) = (-1)^n* (A000032(n) - 4).

a(n+3) = -a(n) -(-1)^n*A022112(n).

a(n) = -2*a(n-1) + a(n-3). - Colin Barker, Jun 23 2014

G.f.: -(5*x^2-x-2) / ((x+1)*(x^2-x-1)). - Colin Barker, Jun 23 2014

PROG

(PARI) Vec(-(5*x^2-x-2)/((x+1)*(x^2-x-1)) + O(x^100)) \\ Colin Barker, Jun 23 2014

CROSSREFS

Cf. A000045, A000032, A000204.

Sequence in context: A082839 A130717 A137396 * A178245 A167666 A115352

Adjacent sequences:  A244210 A244211 A244212 * A244214 A244215 A244216

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Jun 23 2014

STATUS

approved

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Last modified July 19 08:12 EDT 2019. Contains 325155 sequences. (Running on oeis4.)