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, 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

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