A027976 n-th diagonal sum of right justified array T given by A027960.

1, 1, 4, 6, 10, 18, 29, 47, 78, 126, 204, 332, 537, 869, 1408, 2278, 3686, 5966, 9653, 15619, 25274, 40894, 66168, 107064, 173233, 280297, 453532, 733830, 1187362, 1921194, 3108557, 5029751, 8138310, 13168062, 21306372, 34474436, 55780809, 90255245, 146036056, 236291302, 382327358

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 (1,1,1,-1,-1).

Formula

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

From G. C. Greubel, Sep 26 2019: (Start)

a(n) = (Fibonacci(n) + 4*Fibonacci(n+1) - A102283(n) - 2)/2.

a(n) = (Fibonacci(n+1) + Lucas(n+2) - 2*sin(2*Pi*n/3)/sqrt(3) - 2)/2. (End)

Maple

seq(coeff(series((1 + 2*x^2)/((1-x^3)*(1-x-x^2)), x, n+1), x, n), n = 0..40); # G. C. Greubel, Sep 26 2019

Mathematica

LinearRecurrence[{1, 1, 1, -1, -1}, {1, 1, 4, 6, 10}, 41] (* or *) Table[ (Fibonacci[n+1] +LucasL[n+2] -2*Sin[2*Pi*n/3]/Sqrt[3] -2)/2, {n, 0, 40}] (* G. C. Greubel, Sep 26 2019 *)

Prog

(PARI) my(x='x+O('x^40)); Vec((1 + 2*x^2)/((1-x^3)*(1-x-x^2))) \\ G. C. Greubel, Sep 26 2019
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1 + 2*x^2)/((1-x^3)*(1-x-x^2)) )); // G. C. Greubel, Sep 26 2019
(Sage)
def A027976_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P((1 + 2*x^2)/((1-x^3)*(1-x-x^2))).list()
A027976_list(40) # G. C. Greubel, Sep 26 2019
(GAP) a:=[1, 1, 4, 6, 10];; for n in [6..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]-a[n-4]-a[n-5]; od; a; # G. C. Greubel, Sep 26 2019

Crossrefs

Cf. A000032, A000045, A004695, A027960, A102283.

Sequence in context: A165186 A310590 A108232 * A108900 A076995 A096817

Adjacent sequences: A027973 A027974 A027975 * A027977 A027978 A027979

Keyword

nonn

Author

Clark Kimberling

Extensions

Terms a(28) onward added by G. C. Greubel, Sep 26 2019

Status

approved