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A027975 a(n) is the n-th diagonal sum of left justified array T given by A027960. 1
1, 1, 4, 5, 8, 12, 16, 23, 31, 42, 57, 76, 102, 136, 181, 241, 320, 425, 564, 748, 992, 1315, 1743, 2310, 3061, 4056, 5374, 7120, 9433, 12497, 16556, 21933, 29056, 38492, 50992, 67551, 89487, 118546, 157041, 208036, 275590, 365080, 483629, 640673, 848712, 1124305, 1489388, 1973020 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
G.f.: (1 + 2*x^2)/((1-x)*(1-x^2-x^3)).
a(n) = a(n-2) + a(n-3) + 3. - Greg Dresden, May 18 2020
MAPLE
seq(coeff(series((1+2*x^2)/((1-x)*(1-x^2-x^3)), x, n+1), x, n), n = 0..40); # G. C. Greubel, Sep 26 2019
MATHEMATICA
CoefficientList[Series[(1+2*x^2)/((1-x)*(1-x^2-x^3)), {x, 0, 40}], x] (* or *) LinearRecurrence[{1, 1, 0, -1}, {1, 1, 4, 5}, 41] (* G. C. Greubel, Sep 26 2019 *)
PROG
(PARI) my(x='x+O('x^40)); Vec((1+2*x^2)/((1-x)*(1-x^2-x^3))) \\ G. C. Greubel, Sep 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+2*x^2)/((1-x)*(1-x^2-x^3)) )); // G. C. Greubel, Sep 26 2019
(Sage)
def A027975_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+2*x^2)/((1-x)*(1-x^2-x^3)) ).list()
A027975_list(40) # G. C. Greubel, Sep 26 2019
(GAP) a:=[1, 1, 4, 5];; for n in [5..40] do a[n]:=a[n-1]+a[n-2]-a[n-4]; od; a; # G. C. Greubel, Sep 26 2019
CROSSREFS
Cf. A027960.
Sequence in context: A190675 A188077 A370428 * A011980 A260163 A362560
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(32) onward added by G. C. Greubel, Sep 26 2019
STATUS
approved

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Last modified March 29 19:31 EDT 2024. Contains 371281 sequences. (Running on oeis4.)