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A027976 n-th diagonal sum of right justified array T given by A027960. 2
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 (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 (1,1,1,-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

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)