OFFSET
0,1
LINKS
Robert Israel, Table of n, a(n) for n = 0..3399
Daniel Birmajer, Juan B. Gil, and 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
a(n) = Sum_{r root of x^3-x^2-x-1} r^n/(-r^2+r+2). - Fabian Pereyra, Nov 21 2024
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
KEYWORD
easy,nonn,changed
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Aug 06 2002
STATUS
approved