A073728 a(n) = Sum_{k=0..n} S(k), where S(n) are the tribonacci generalized numbers A001644.

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

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