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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
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
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]
LinearRecurrence[{-1, 2}, {0, 1, 3}, 40] (* Harvey P. Dale, Jan 14 2020 *)
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: A033465 A096431 A370857 * A280332 A279939 A337748
KEYWORD
easy,sign
AUTHOR
Paul Curtz, Dec 10 2009
EXTENSIONS
Mathematica program by Olivier Gérard, Jul 06 2011
STATUS
approved