OFFSET
0,3
COMMENTS
Unsigned version of A077920.
The sequence is the INVERT transform of the aerated even-indexed Fibonacci numbers (i.e., of (1, 0, 3, 0, 8, 0, ...)). Sequence A131322 is the INVERT transform of the aerated odd-indexed Fibonacci numbers. - Gary W. Adamson, Feb 07 2014
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,0,-1).
FORMULA
G.f.: 1/(1-x-3*x^2+x^4).
MAPLE
seq(coeff(series(1/(1-x-3*x^2+x^4), x, n+1), x, n), n = 0..35); # G. C. Greubel, Dec 25 2019
MATHEMATICA
LinearRecurrence[{1, 3, 0, -1}, {1, 1, 4, 7}, 35] (* G. C. Greubel, Dec 25 2019 *)
CoefficientList[Series[1/(1-x-3x^2+x^4), {x, 0, 30}], x] (* Harvey P. Dale, Feb 01 2022 *)
PROG
(PARI) my(x='x+O('x^35)); Vec(1/(1-x-3*x^2+x^4)) \\ G. C. Greubel, Dec 25 2019
(Magma) I:=[1, 1, 4, 7]; [n le 2 select I[n] else Self(n-1) +3*Self(n-2) -Self(n-4): n in [1..35]]; // G. C. Greubel, Dec 25 2019
(Sage)
def A124400_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 1/(1-x-3*x^2+x^4) ).list()
A124400_list(35) # G. C. Greubel, Dec 25 2019
(GAP) a:=[1, 1, 4, 7];; for n in [5..35] do a[n]:=a[n-1]+3*a[n-2]-a[n-4]; od; a; # G. C. Greubel, Dec 25 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Dec 14 2006
STATUS
approved