|
| |
|
|
A001630
|
|
Tetranacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=a(1)=0, a(2)=1, a(3)=2.
(Formerly M0795 N0301)
|
|
9
| |
|
|
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, 2187020050
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,4
|
|
|
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).
|
|
|
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.
Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,1).
|
|
|
FORMULA
| a(n) = A000078(n)+A000078(n+1) = a(n-1)+A000078(n+1)-A000078(n-1). - Henry Bottomley
a(0)=a(1)=0, a(2)=1, a(3)=2, a(4)=3; a(n) = 2*a(n-1)-a(n-5), n>=5. [From Vincenzo Librandi, Dec 21 2010]
|
|
|
MAPLE
| A001630:=-z**2*(1+z)/(-1+z+z**2+z**3+z**4); [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]
|
|
|
MATHEMATICA
| 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]
|
|
|
CROSSREFS
| Cf. A000032.
Sequence in context: A068012 A019138 A154324 * A164363 A103341 A023675
Adjacent sequences: A001627 A001628 A001629 * A001631 A001632 A001633
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Henry Bottomley (se16(AT)btinternet.com), Oct 09 2000
|
| |
|
|
