|
| |
|
|
A001634
|
|
a(n) = a(n-2) + a(n-3) + a(n-4).
(Formerly M0746 N0281)
|
|
2
| |
|
|
0, 2, 3, 6, 5, 11, 14, 22, 30, 47, 66, 99, 143, 212, 308, 454, 663, 974, 1425, 2091, 3062, 4490, 6578, 9643, 14130, 20711, 30351, 44484, 65192, 95546, 140027, 205222, 300765, 440795, 646014, 946782, 1387574, 2033591, 2980370, 4367947, 6401535, 9381908
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| E.-B. Escott, Reply to Query 1484, L'Interm\'{e}diaire des Math\'{e}maticiens, 8 (1901), 63-64.
Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
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
| T. D. Noe, Table of n, a(n) for n=0..500
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.
|
|
|
FORMULA
| G.f.: x(2+3x+4x^2)/(1-x^2-x^3-x^4).
|
|
|
MAPLE
| A001634:=-z*(2+3*z+4*z**2)/(1+z)/(z**3+z-1); [S. Plouffe in his 1992 dissertation.]
(Maple) a := n -> (Matrix([[0, 4, -1, -1]]). Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [0, 1, 1, 1][i] else 0 fi)^n)[1, 1] ; seq (a(n), n=0..40); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 01 2008]
|
|
|
MATHEMATICA
| LinearRecurrence[{0, 1, 1, 1}, {0, 2, 3, 6}, 100] (* From Vladimir Joseph Stephan Orlovsky, Jul 01 2011 *)
|
|
|
PROG
| (PARI) a(n)=if(n<0, 0, polcoeff(x*(2+3*x+4*x^2)/(1-x^2-x^3-x^4)+x*O(x^n), n))
|
|
|
CROSSREFS
| Cf. A013979.
Sequence in context: A133477 A039653 A106379 * A172989 A095113 A002517
Adjacent sequences: A001631 A001632 A001633 * A001635 A001636 A001637
|
|
|
KEYWORD
| nonn,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
