A001687 a(n) = a(n-2) + a(n-5).
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
Keywords
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
- T. D. Noe, Table of n, a(n) for n = 0..1000
- 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.
- INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 405
- 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
- E. Wilson, The Scales of Mt. Meru
- R. Yanco, Letter and Email to N. J. A. Sloane, 1994
- R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994. (Annotated scanned copy)
- Index entries for two-way infinite sequences
- Index entries for linear recurrences with constant coefficients, signature (0, 1, 0, 0, 1).
Crossrefs
Cf. A005686.
Programs
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Maple
A001687:=-z/(-1+z**2+z**5); # Simon 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] (* Harvey P. Dale, Apr 06 2011 *) LinearRecurrence[{0, 1, 0, 0, 1}, {0, 1, 0, 1, 0}, 100] (* T. D. Noe, Aug 09 2012 *) -
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 */
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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 */
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
Comments