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A027959 a(n) = Sum_{k=m..n} T(k,n-k), where m = floor((n+1)/2); a(n) is the n-th diagonal-sum of left justified array T given by A027948. 1
1, 1, 2, 3, 5, 7, 12, 16, 27, 37, 59, 85, 129, 192, 285, 428, 634, 949, 1412, 2104, 3140, 4671, 6973, 10378, 15478, 23058, 34362, 51216, 76305, 113736, 169465, 252561, 376362, 560851, 835821, 1245503, 1856132, 2765976, 4121947 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,3,1,-3,-1,1).

FORMULA

G.f.: x*(1+x-x^2-x^3+x^4)/((1-x)*(1+x)*(1-2*x^2-x^3+x^4)). - Colin Barker, Nov 25 2014

MAPLE

seq(coeff(series(x*(1+x-x^2-x^3+x^4)/((1-x^2)*(1-2*x^2-x^3+x^4)), x, n+1), x, n), n = 1..40); # G. C. Greubel, Sep 30 2019

MATHEMATICA

T[n_, k_]:= If[k==n, 1, Sum[Binomial[k+j, 2*j-1], {j, 0, n-k}]]; Table[Sum[T[k, n-k], {k, Floor[(n-1)/2], n}], {n, 0, 40}] (* G. C. Greubel, Sep 30 2019 *)

PROG

(PARI) my(x='x+O('x^40)); Vec(x*(1+x-x^2-x^3+x^4)/((1-x^2)*(1-2*x^2-x^3+x^4))) \\ G. C. Greubel, Sep 30 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( x*(1+x-x^2-x^3+x^4)/((1-x^2)*(1-2*x^2-x^3+x^4)) )); // G. C. Greubel, Sep 30 2019

(Sage)

def A027959_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( x*(1+x-x^2-x^3+x^4)/((1-x^2)*(1-2*x^2-x^3+x^4)) ).list()

a=A027959_list(40); a[1:] # G. C. Greubel, Sep 30 2019

(GAP) a:=[1, 1, 2, 3, 5, 7];; for n in [7..40] do a[n]:=3*a[n-2]+a[n-3] -3*a[n-4]-a[n-5]+a[n-6]; od; a; # G. C. Greubel, Sep 30 2019

CROSSREFS

Cf. A027948.

Sequence in context: A179822 A319769 A326083 * A060730 A308928 A308992

Adjacent sequences:  A027956 A027957 A027958 * A027960 A027961 A027962

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 11 18:34 EST 2019. Contains 329925 sequences. (Running on oeis4.)