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
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).
Programs
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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
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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] -
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
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