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A075676 Sequences A001644 and A000073 interleaved. 1
3, 1, 3, 2, 11, 7, 39, 24, 131, 81, 443, 274, 1499, 927, 5071, 3136, 17155, 10609, 58035, 35890, 196331, 121415, 664183, 410744, 2246915, 1389537, 7601259, 4700770, 25714875, 15902591, 86992799, 53798080, 294294531, 181997601 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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(n) = A000073(n) if n odd, a(n) = A001644(n) if n even.

a(n) = ((1-(-1)^n)*T(n) + (1+(-1)^n)*S(n))/2, where T(n) = A000073(n), S(n) =  A001644(n).

a(n) = 3*a(n-2) + a(n-4) + a(n-6), a(0)=3, a(1)=1, a(2)=3, a(3)=2, a(4)=11, a(5)=7.

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

a(n) = T(n) + (1+(-1)^n)*(T(n-1) + (3/2)*T(n-2)).

MATHEMATICA

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

LinearRecurrence[{0, 3, 0, 1, 0, 1}, {3, 1, 3, 2, 11, 7}, 40] (* Harvey P. Dale, May 01 2014 *)

PROG

(PARI) my(x='x+O('x^40)); Vec((3+x-6*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); Coefficients(R!( (3+x- 6*x^2-x^3-x^4)/(1-3*x^2-x^4-x^6) )); // G. C. Greubel, Apr 21 2019

(Sage) ((3+x-6*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, A075536.

Sequence in context: A058589 A112164 A300580 * A298262 A124814 A122567

Adjacent sequences:  A075673 A075674 A075675 * A075677 A075678 A075679

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Sep 24 2002

STATUS

approved

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Last modified January 23 19:45 EST 2020. Contains 331175 sequences. (Running on oeis4.)