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A171501 Inverse binomial transform of A084640. 1
0, 1, 3, -1, 7, -9, 23, -41, 87, -169, 343, -681, 1367, -2729, 5463, -10921, 21847, -43689, 87383, -174761, 349527, -699049, 1398103, -2796201, 5592407, -11184809, 22369623, -44739241, 89478487, -178956969, 357913943, -715827881 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) and differences are

0,     1,   3,  -1,    7,   -9,

1,     2,  -4,   8,  -16,   32,  =(-1)^(n+1) * A171449(n),

1,    -6,  12, -24,   48,  -96,

-7,   18, -36,  72, -144,  288,

25,  -54, 108, -216, 432, -864,

Vertical: 1) 0 followed with A168589(n).

          2) (-1 followed with A008776(n) ) signed. See A025192(n).

Main diagonal: see A167747(1+n). - Paul Curtz, Jun 16 2011

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

FORMULA

a(n) = A140966(n), n>0.

G.f.: x*(1+4*x) / ( (1+2*x)*(1-x) ). - R. J. Mathar, Jun 14 2011

a(1+n)= (-1)^(1+n) * A001045(1+n) + 2. - Paul Curtz Jun 16 2011

MATHEMATICA

CoefficientList[Series[x*(1 + 4*x)/((1 + 2*x)*(1 - x)), {x, 0, 30}], x]

PROG

(MAGMA) I:=[0, 1, 3]; [n le 3 select I[n] else -Self(n-1) + 2*Self(n-2): n in [1..40]]; // Vincenzo Librandi, Oct 18 2012

CROSSREFS

Sequence in context: A011308 A033465 A096431 * A280332 A279939 A286511

Adjacent sequences:  A171498 A171499 A171500 * A171502 A171503 A171504

KEYWORD

easy,sign

AUTHOR

Paul Curtz, Dec 10 2009

EXTENSIONS

Mathematica program by Olivier Gérard, Jul 06 2011

STATUS

approved

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Last modified September 15 14:38 EDT 2019. Contains 327078 sequences. (Running on oeis4.)