A001687 a(n) = a(n-2) + a(n-5). (Formerly M0147 N0059)

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

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R. Yanco and A. Bagchi, K-th order maximal independent sets in path and cycle graphs, Unpublished manuscript, 1994.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).

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

Adjacent sequences: A001684 A001685 A001686 * A001688 A001689 A001690

Keyword

nonn

Author

N. J. A. Sloane, following a suggestion from Robert G. Wilson v

Status

approved