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A073728 a(n) = Sum_{k=0..n} S(k), where S(n) are the tribonacci generalized numbers A001644. 2
3, 4, 7, 14, 25, 46, 85, 156, 287, 528, 971, 1786, 3285, 6042, 11113, 20440, 37595, 69148, 127183, 233926, 430257, 791366, 1455549, 2677172, 4924087, 9056808, 16658067, 30638962, 56353837, 103650866, 190643665, 350648368, 644942899 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Robert Israel, Table of n, a(n) for n = 0..3399

Daniel Birmajer, Juan B. Gil, Michael D. Weiner, Linear recurrence sequences with indices in arithmetic progression and their sums, arXiv:1505.06339 [math.NT], 2015.

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

FORMULA

a(n) = a(n-1) + a(n-2) + a(n-3), a(0)=3, a(1)=4, a(2)=7.

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

a(n) = 3*T(n+1) + T(n), where T(n) are the tribonacci numbers A000073.

a(n) = (S(n+3) - S(n+1))/2, where S(n) = A001644(n). - Michael D. Weiner, Mar 27 2015

MAPLE

A:= gfun[rectoproc]({a(n)=a(n-1)+a(n-2)+a(n-3), a(0)=3, a(1)=4, a(2)=7}, a(n), remember):

seq(A(n), n=0..100); # Robert Israel, Mar 26 2015

MATHEMATICA

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

PROG

(MAGMA) I:=[3, 4, 7]; [n le 3 select I[n] else Self(n-1)+Self(n-2) +Self(n-3): n in [1..40]]; // Vincenzo Librandi, Mar 27 2015

(PARI) my(x='x+O('x^40)); Vec((3+x)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 09 2019

(Sage) ((3+x)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 09 2019

CROSSREFS

Cf. A001644, A000073.

Sequence in context: A319548 A095063 A003242 * A132753 A132407 A070035

Adjacent sequences:  A073725 A073726 A073727 * A073729 A073730 A073731

KEYWORD

easy,nonn

AUTHOR

Mario Catalani (mario.catalani(AT)unito.it), Aug 06 2002

STATUS

approved

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Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)