A027947 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 A027935.

1, 1, 2, 3, 4, 7, 9, 15, 21, 32, 48, 70, 107, 156, 236, 349, 521, 778, 1155, 1728, 2567, 3833, 5707, 8505, 12680, 18884, 28158, 41943, 62520, 93160, 138825, 206897, 308290, 459459, 684652, 1020311, 1520473, 2265815, 3376605

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 (0,2,1,-1).

Formula

G.f.: (1 + x)/(1 - 2*x^2 - x^3 + x^4).

Maple

seq(coeff(series((1+x)/(1-2*x^2-x^3+x^4), x, n+1), x, n), n = 0..40); # G. C. Greubel, Sep 29 2019

Mathematica

LinearRecurrence[{0, 2, 1, -1}, {1, 1, 2, 3}, 40] (* G. C. Greubel, Sep 29 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1+x)/(1-2*x^2-x^3+x^4)) \\ G. C. Greubel, Sep 29 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)/(1-2*x^2-x^3+x^4) )); // G. C. Greubel, Sep 29 2019
(Sage)
def A027947_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1+x)/(1-2*x^2-x^3+x^4)).list()
A027947_list(40) # G. C. Greubel, Sep 29 2019
(GAP) a:=[1, 1, 2, 3];; for n in [5..40] do a[n]:=2*a[n-2]+a[n-3]-a[n-4]; od; a; # G. C. Greubel, Sep 29 2019

Crossrefs

Cf. A027935.

Sequence in context: A108809 A276846 A303665 * A324736 A293853 A067236

Adjacent sequences: A027944 A027945 A027946 * A027948 A027949 A027950

Keyword

nonn

Author

Clark Kimberling

Status

approved