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A081172
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Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) starting with 1,1,0.
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5
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1, 1, 0, 2, 3, 5, 10, 18, 33, 61, 112, 206, 379, 697, 1282, 2358, 4337, 7977, 14672, 26986, 49635, 91293, 167914, 308842, 568049, 1044805, 1921696, 3534550, 6501051, 11957297, 21992898, 40451246, 74401441, 136845585, 251698272, 462945298, 851489155
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Completes the set of tribonacci numbers starting with 0's and 1's in the first three terms: 0,0,0 trivial; 0,0,1 A000073; 0,1,0 A001590; 0,1,1 A000073 starting at a(1); 1,0,0 A000073 starting at a(-1); 1,0,1 A001590; 1,1,0 this sequence; 1,1,1 A000213.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,500
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FORMULA
| G.f.: (-1+2*x^2)/(-1+x+x^2+x^3). a(n)=A000073(n+2)-2*A00073(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 27 2009]
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MATHEMATICA
| LinearRecurrence[{1, 1, 1}, {1, 1, 0}, 100] (* From Vladimir Joseph Stephan Orlovsky, June 07 2011 *)
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PROG
| (PARI) { a1=1; a2=1; a3=0; write("b081172.txt", 0, " ", a1); write("b081172.txt", 1, " ", a2); write("b081172.txt", 2, " ", a3); for(n=3, 500, a=a1+a2+a3; a1=a2; a2=a3; a3=a; write("b081172.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Mar 20 2009]
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CROSSREFS
| Cf. A000073, A000213, A001590, A020992.
Sequence in context: A195507 A117222 A199594 * A030032 A002661 A065053
Adjacent sequences: A081169 A081170 A081171 * A081173 A081174 A081175
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KEYWORD
| nonn,easy
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AUTHOR
| Harry J. Smith (hjsmithh(AT)sbcglobal.net), Apr 19 2003
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