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A001584 A generalized Fibonacci sequence.
(Formerly M0235 N0080)
+0
1
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 4, 4, 4, 7, 7, 8, 12, 12, 16, 21, 21, 31, 37, 38, 58, 65, 71, 106, 114, 135, 191, 201, 257, 341, 359, 485, 605, 652, 904, 1070, 1202, 1664, 1894, 2237, 3029, 3370, 4176, 5464, 6048, 7779, 9793, 10963, 14411, 17492, 20054, 26507, 31239, 36924, 48396 (list; graph; listen)
OFFSET

0,9

REFERENCES

V. C. Harris, Generalized Fibonacci sequences associated with a generalized Pascal triangle, Fib. Quart., 4 (1966), 241-248.

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..1000

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.: (1+x+x^2-x^3-x^4-x^5)/(1-2*x^3+x^6-x^8).

MAPLE

A001584:=(z-1)*(z**2+z+1)**2/(z**4-z**3+1)/(z**4+z**3-1); [S. Plouffe in his 1992 dissertation.]

CROSSREFS

Cf. A017817.

Sequence in context: A029047 A007294 A053282 this_sequence A112801 A089873 A096323

Adjacent sequences: A001581 A001582 A001583 this_sequence A001585 A001586 A001587

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

More terms from David W. Wilson (davidwwilson(AT)comcast.net)

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Last modified December 10 00:48 EST 2009. Contains 170565 sequences.


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