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A001687
a(n) = a(n-2) + a(n-5).
(Formerly M0147 N0059)
11
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
OFFSET
0,9
COMMENTS
a(n+1) is the number of compositions of n into parts 2 and 5. [Joerg Arndt, Mar 15 2013]
REFERENCES
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
Dorota Bród, On trees with unique locating kernels, Boletín de la Sociedad Matemática Mexicana (2021) Vol. 27, Art. No. 61.
T. M. Green, Recurrent sequences and Pascal's triangle, Math. Mag., 41 (1968), 13-21.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994. (Annotated scanned copy)
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, Jul 04 2004
G.f.: -x/( x^5 - 1 + 5*x^2/Q(0) ) where Q(k) = x + 5 + k*(x+1) - x*(k+1)*(k+6)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Mar 15 2013
MAPLE
A001687:=-z/(-1+z**2+z**5); # Simon Plouffe in his 1992 dissertation
MATHEMATICA
CoefficientList[Series[x/(1-x^2-x^5), {x, 0, 60}], x] (* or *) Nest[ Append[#, #[[-5]]+#[[-2]]]&, {0, 1, 0, 1, 0}, 60] (* Harvey P. Dale, Apr 06 2011 *)
LinearRecurrence[{0, 1, 0, 0, 1}, {0, 1, 0, 1, 0}, 100] (* T. D. Noe, Aug 09 2012 *)
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); /* Vladimir Kruchinin, May 24 2011 */
CROSSREFS
Cf. A005686.
Sequence in context: A328171 A029139 A100927 * A159072 A116928 A239948
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, following a suggestion from Robert G. Wilson v
STATUS
approved