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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
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

Table of n, a(n) for n=0..32.

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).

MATHEMATICA

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

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

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..35]]; // Vincenzo Librandi, Feb 04 2016

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 October 18 05:17 EDT 2018. Contains 316304 sequences. (Running on oeis4.)