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Search: id:A001630
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| A001630 |
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Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) +a(n-4).
(Formerly M0795 N0301)
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+0
9
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| 0, 0, 1, 2, 3, 6, 12, 23, 44, 85, 164, 316, 609, 1174, 2263, 4362, 8408, 16207, 31240, 60217, 116072, 223736, 431265, 831290, 1602363, 3088654, 5953572, 11475879, 22120468, 42638573, 82188492, 158423412, 305370945, 588621422, 1134604271
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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W. C. Lynch, The t-Fibonacci numbers and polyphase sorting, Fib. Quart., 8 (1970), pp. 6ff.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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a(n) = A000078(n)+A000078(n+1) = a(n-1)+A000078(n+1)-A000078(n-1) - Henry Bottomley
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MAPLE
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A001630:=-z**2*(1+z)/(-1+z+z**2+z**3+z**4); [Conjectured by S. Plouffe in his 1992 dissertation.]
(Maple) a := proc(n) option operator; local M; M := Matrix(4, (i, j)-> if (i=j-1) or j=1 then 1 else 0 fi)^n; M[1, 4]+M[1, 3] end; seq (a(n), n=0..34); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 2008]
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MATHEMATICA
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a=0; b=0; c=1; d=2; lst={a, b, c, d}; Do[e=a+b+c+d; AppendTo[lst, e]; a=b; b=c; c=d; d=e, {n, 4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 30 2008]
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CROSSREFS
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Sequence in context: A068012 A019138 A154324 this_sequence A164363 A103341 A023675
Adjacent sequences: A001627 A001628 A001629 this_sequence A001631 A001632 A001633
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Henry Bottomley (se16(AT)btinternet.com), Oct 09 2000
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