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A001687
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a(n) = a(n-2) + a(n-5).
(Formerly M0147 N0059)
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2
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0, 1, 0, 1, 0, 1, 1, 1, 2, 1, 3, 2, 4, 4, 5, 7, 7, 11, 11, 16, 18, 23, 29, 34, 45, 52, 68, 81, 102, 126, 154, 194, 235, 296, 361, 450, 555, 685, 851, 1046, 1301, 1601, 1986, 2452, 3032, 3753, 4633, 5739, 7085, 8771, 10838, 13404, 16577, 20489, 25348, 31327
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,9
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REFERENCES
| T. M. Green, Recurrent sequences and Pascal's triangle, Math. Mag., 41 (1968), 13-21.
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
| INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 405
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.
E. Wilson, The Scales of Mt. Meru
Index entries for two-way infinite sequences
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FORMULA
| G.f.: x/(1-x^2-x^5).
G.f. A(x) satisfies 1+x^4*A(x) = 1/(1-x^5-x^7-x^9-....) - Jon Perry (perry(AT)globalnet.co.uk), Jul 04 2004
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MAPLE
| A001687:=-z/(-1+z**2+z**5); [S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| CoefficientList[Series[x/(1-x^2-x^5), {x, 0, 60}], x] (* or *) Nest[ Append[#, #[[-5]]+#[[-2]]]&, {0, 1, 0, 1, 0}, 60] (* From Harvey P. Dale, Apr 06 2011 *)
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PROG
| (PARI) a(n)=if(n<0, polcoeff(x^4/(1+x^3-x^5)+x^-n*O(x), -n), polcoeff(x/(1-x^2-x^5)+x^n*O(x), n)) /* Michael Somos, Jul 15 2004 */
(Maxima)
a(n):=sum(if mod(n-5*k, 3)=0 then binomial(k, (5*k-n)/3) else 0, k, 1, n); [From Vladimir Kruchinin (kru(AT)ie.tusur.ru), May 24 2011]
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CROSSREFS
| Cf. A005686.
Sequence in context: A144693 A029139 A100927 * A159072 A116928 A034391
Adjacent sequences: A001684 A001685 A001686 * A001688 A001689 A001690
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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