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A075536 a(n) = ((1+(-1)^n)*T(n+1) + (1-(-1)^n)*S(n))/2, where T(n) = tribonacci numbers A000073, S(n) = generalized tribonacci numbers A001644. 2
0, 1, 1, 7, 4, 21, 13, 71, 44, 241, 149, 815, 504, 2757, 1705, 9327, 5768, 31553, 19513, 106743, 66012, 361109, 223317, 1221623, 755476, 4132721, 2555757, 13980895, 8646064, 47297029, 29249425, 160004703, 98950096, 541292033, 334745777 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

a(2n) = A073717(n) = A000073(2n+1).

a(2n+1) = A001644(2n+1).

a(n) = 3*a(n-2) + a(n-4) + a(n-6), a(0)=0, a(1)=1, a(2)=1, a(3)=7, a(4)=4, a(5)=21.

O.g.f.: x*(1 + x + 4*x^2 + x^3 - x^4)/(1 - 3*x^2 - x^4 - x^6).

MAPLE

A075536 := proc(n)

    if type(n, 'even') then

        A000073(n+1) ;

    else

        A001644(n) ;

    end if;

end proc:

seq(A075536(n), n=0..80) ; # R. J. Mathar, Aug 05 2021

MATHEMATICA

CoefficientList[Series[(x+x^2+4x^3+x^4-x^5)/(1-3x^2-x^4-x^6), {x, 0, 40}], x]

LinearRecurrence[{0, 3, 0, 1, 0, 1}, {0, 1, 1, 7, 4, 21}, 40] (* Harvey P. Dale, Jul 10 2012 *)

PROG

(PARI) my(x='x+O('x^40)); concat([0], Vec(x*(1+x+4*x^2+x^3-x^4)/(1-3*x^2-x^4-x^6))) \\ G. C. Greubel, Apr 21 2019

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); [0] cat Coefficients(R!( x*(1+x+4*x^2+x^3-x^4)/(1-3*x^2-x^4-x^6) )); // G. C. Greubel, Apr 21 2019

(Sage) (x*(1+x+4*x^2+x^3-x^4)/(1-3*x^2-x^4-x^6)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 21 2019

CROSSREFS

Cf. A000073, A001644, A005013, A005247.

Sequence in context: A279998 A063632 A147601 * A280336 A085047 A213831

Adjacent sequences:  A075533 A075534 A075535 * A075537 A075538 A075539

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Sep 23 2002

EXTENSIONS

Index in definition corrected. - R. J. Mathar, Aug 05 2021

STATUS

approved

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Last modified October 6 09:29 EDT 2022. Contains 357263 sequences. (Running on oeis4.)