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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. 0

%I

%S 5,7,9,21,37,67,125,229,421,775,1425,2621,4821,8867,16309,29997,55173,

%T 101479,186649,343301,631429,1161379,2136109,3928917,7226405,13291431,

%U 24446753,44964589,82702773,152114115,279781477,514598365,946493957

%N a(n) = a(n - 1) + a(n - 2) + a(n - 3) for n>2, a(0)=5, a(1)=7, a(2)=9.

%C Tribonacci sequence beginning 5, 7, 9.

%C 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).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TribonacciNumber.html">Tribonacci Number</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1)

%F G.f.: (5 + 2*x - 3*x^2)/(1 - x - x^2 - x^3).

%t LinearRecurrence[{1, 1, 1}, {5, 7, 9}, 33]

%t RecurrenceTable[{a[0] == 5, a[1] == 7, a[2] == 9, a[n] == a[n - 1] + a[n - 2] + a[n - 3]}, a, {n, 32}]

%o (MAGMA) I:=[5,7,9]; [n le 3 select I[n] else Self(n-1)+Self(n-2)+Self(n-3): n in [1..35]]; // _Vincenzo Librandi_, Feb 04 2016

%Y 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).

%K nonn,easy,less

%O 0,1

%A _Ilya Gutkovskiy_, Feb 04 2016

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Last modified October 17 12:01 EDT 2018. Contains 316279 sequences. (Running on oeis4.)