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 A268410 a(n) = a(n - 1) + a(n - 2) + a(n - 3) for n>2, a(0)=5, a(1)=7, a(2)=9. 1
 5, 7, 9, 21, 37, 67, 125, 229, 421, 775, 1425, 2621, 4821, 8867, 16309, 29997, 55173, 101479, 186649, 343301, 631429, 1161379, 2136109, 3928917, 7226405, 13291431, 24446753, 44964589, 82702773, 152114115, 279781477, 514598365, 946493957 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Tribonacci sequence beginning 5, 7, 9. In general, the ordinary generating function for the recurrence relation b(n) = b(n-1) + b(n-2) + b(n-3), with n>2 and b(0)=k, b(1)=m, b(2)=q, is (k + (m-k)*x  + (q-m-k)*x^2)/(1 - x - x^2 - x^3). LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Tribonacci Number Index entries for linear recurrences with constant coefficients, signature (1,1,1) FORMULA G.f.: (5 + 2*x - 3*x^2)/(1 - x - x^2 - x^3). a(n) = 3*K(n) - 4*T(n+1) + 8*T(n), where K(n) = A001644(n) and T(n) =A000073(n+1). - G. C. Greubel, Apr 23 2019 MATHEMATICA LinearRecurrence[{1, 1, 1}, {5, 7, 9}, 40] RecurrenceTable[{a[0]==5, a[1]==7, a[2]==9, a[n]==a[n-1]+a[n-2]+a[n-3]}, a, {n, 40}] PROG (MAGMA) I:=[5, 7, 9]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 04 2016 (PARI) my(x='x+O('x^40)); Vec((5+2*x-3*x^2)/(1-x-x^2-x^3)) \\ G. C. Greubel, Apr 23 2019 (Sage) ((5+2*x-3*x^2)/(1-x-x^2-x^3)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 23 2019 (GAP) a:=[5, 7, 9];; for n in [4..40] do a[n]:=a[n-1]+a[n-2]+a[n-3]; od; a; # G. C. Greubel, Apr 23 2019 CROSSREFS Cf. similar sequences with initial values (p,q,r): A000073 (0,0,1), A081172 (1,1,0), A001590 (0,1,0; also 1,2,3), A214899 (2,1,2), A001644 (3,1,3), A145027 (2,3,4), A000213 (1,1,1), A141036 (2,1,1), A141523 (3,1,1), A214727 (1,2,2), A214825 (1,3,3), A214826 (1,4,4), A214827 (1,5,5), A214828 (1,6,6), A214829 (1,7,7), A214830 (1,8,8), A214831 (1,9,9). Sequence in context: A186406 A068332 A276734 * A029650 A049307 A050113 Adjacent sequences:  A268407 A268408 A268409 * A268411 A268412 A268413 KEYWORD nonn,easy,less AUTHOR Ilya Gutkovskiy, Feb 04 2016 STATUS approved

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Last modified July 24 00:28 EDT 2021. Contains 346265 sequences. (Running on oeis4.)