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.

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

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