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 A073728 a(n) = Sum_{k=0..n} S(k), where S(n) are the tribonacci generalized numbers A001644. 1
 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 preprint, 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 CROSSREFS Cf. A001644, A000073. Sequence in context: A062203 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 January 19 16:49 EST 2019. Contains 319309 sequences. (Running on oeis4.)