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A001631
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Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) +a(n-4).
(Formerly M1081 N0410)
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4
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0, 0, 1, 0, 1, 2, 4, 7, 14, 27, 52, 100, 193, 372, 717, 1382, 2664, 5135, 9898, 19079, 36776, 70888, 136641, 263384, 507689, 978602, 1886316, 3635991, 7008598, 13509507, 26040412, 50194508, 96753025, 186497452, 359485397, 692930382, 1335666256, 2574579487
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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REFERENCES
| 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
| 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.
Harvey P. Dale, Table of n, a(n) for n = 0..1000
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FORMULA
| G.f.: ((x-1)*x^2)/(x^4+x^3+x^2+x-1) [From Harvey P. Dale, Oct 21 2011]
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MAPLE
| A001631:=(-1+z)/(-1+z+z**2+z**3+z**4); [Conjectured by S. Plouffe in his 1992 dissertation.]
a:= n-> (Matrix([[0, -1, 2, -1]]). Matrix(4, (i, j)-> `if` (i=j-1 or j=1, 1, 0))^n)[1, 1]: seq (a(n), n=0..35); # Alois P. Heinz, Aug 01 2008
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MATHEMATICA
| LinearRecurrence[{1, 1, 1, 1}, {0, 0, 1, 0}, 100] (* From Vladimir Joseph Stephan Orlovsky, Jul 01 2011 *)
CoefficientList[Series[((-1+x) x^2)/(-1+x+x^2+x^3+x^4), {x, 0, 50}], x] (* From Harvey P. Dale, Oct 21 2011 *)
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CROSSREFS
| First differences of A000078.
Sequence in context: A005594 A123196 A079968 * A108758 A018085 A167751
Adjacent sequences: A001628 A001629 A001630 * A001632 A001633 A001634
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Larry Reeves (larryr(AT)acm.org), Jul 31 2000
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