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A000288
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Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4).
(Formerly M3307 N1332)
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31
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1, 1, 1, 1, 4, 7, 13, 25, 49, 94, 181, 349, 673, 1297, 2500, 4819, 9289, 17905, 34513, 66526, 128233, 247177, 476449, 918385, 1770244, 3412255, 6577333, 12678217, 24438049, 47105854, 90799453, 175021573, 337364929, 650291809, 1253477764
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| For n>=0: a(n+2) is the number of length-n strings with letters {0,1,2,3} where the letter x is followed by at least x zeros, see fxtbook link below. [Joerg Arndt, Apr 08 2011]
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REFERENCES
| B. G. Baumgart, Letter to the editor, Fib. Quart. 2 (1964), 260, 302.
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
| T. D. Noe, Table of n, a(n) for n=0..200
Joerg Arndt, Fxtbook, pp.311-312
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.
Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,1).
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FORMULA
| [a(n), a(n+1), a(n+2), a(n+3)]' = (M^n)*[1 1 1 1]', where M = the 4 X 4 matrix [0 1 0 0 / 0 0 1 0 / 0 0 0 1 / 1 1 1 1]. E.g. [7 13 25 49]' = (M^5)*[1 1 1 1]' = [a(5), a(6), a(7), a(8)]'. Here the prime denotes transpose. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 22 2004.
a(0) = a(1) = a(2) = a(3) = 1, a(4) = 4, a(n) = 2*a(n-1) - a(n-5). [From Vincenzo Librandi, Dec 21 2010]
a(n) = -2*A000078(n)-A000078(n+1)+A000078(n+3). - R. J. Mathar, Apr 07 2011
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MAPLE
| A000288:=(-1+z**2+2*z**3)/(-1+z**2+z**3+z+z**4); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = a[n - 1] + a[n - 2] + a[n - 3] + a[n - 4]; Table[ a[n], {n, 0, 34}] (* Robert G. Wilson v *)
LinearRecurrence[{1, 1, 1, 1}, {1, 1, 1, 1}, 30] (* From Harvey P. Dale, May 23 2011 *)
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CROSSREFS
| Cf. A060455.
Sequence in context: A038391 A090854 A039694 * A074863 A118334 A205538
Adjacent sequences: A000285 A000286 A000287 * A000289 A000290 A000291
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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 Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 27 2005
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