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A027975 a(n) = 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

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: (1 + 2*x^2)/((1-x)*(1-x^2-x^3)).

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: A188095 A190675 A188077 * A011980 A260163 A061765

Adjacent sequences:  A027972 A027973 A027974 * A027976 A027977 A027978

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Terms a(32) onward added by G. C. Greubel, Sep 26 2019

STATUS

approved

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Last modified November 13 02:59 EST 2019. Contains 329085 sequences. (Running on oeis4.)