A308620 Number of states in the evolutionary spatial prisoner's dilemma with n players.

2, 2, 2, 3, 4, 6, 9, 13, 19, 28, 42, 63, 95, 143, 216, 327, 496, 754, 1147, 1747, 2662, 4059, 6192, 9450, 14428, 22034, 33658, 51422, 78573, 120073, 183510, 280485, 428733, 655371, 1001854, 1531567, 2341417, 3579571, 5472565, 8366756

Offset

1,1

Comments

Conjecture: satisfies a linear recurrence having signature (2, 0, -2, 1, 2, -2, 0, 0, 0, -1). - Harvey P. Dale, Aug 21 2021

Links

Table of n, a(n) for n=1..40.

Burger, A. P. ; Van Der Merwe, M.; Van Vuuren, J. H. An asymptotic analysis of the evolutionary spatial prisoner’s dilemma on a path, Discrete Appl. Math. 160, No. 15, 2075-2088 (2012) Table 4.2

Formula

Conjecture: g.f. 2*x -x^2*(-2 +2*x +x^2 -2*x^3 +3*x^5 +x^7 +x^9)/ (x^5+x^2-1)/ (x^5-x^2+2*x-1) .

Maple

A308620 := proc(n)
    add( binomial(n-3*i+2, 2*i-2) +binomial(floor((n-5*i+4)/2)+i-1, i-1), i=1..floor((n+4)/5)) ;
    %+add(binomial(n-3*i-2, 2*i)+binomial(floor((n-5*i-2)/2)+i, i), i=1..floor((n-2)/5)) ;
    %/2+1 ;
    %+add(binomial(n-3*i, 2*i-1), i=1..floor((n+1)/5)) ;
end proc:
seq(A308620(n), n=1..40) ;

Crossrefs

Sequence in context: A333374 A098523 A350514 * A339711 A048185 A368520

Adjacent sequences: A308617 A308618 A308619 * A308621 A308622 A308623

Keyword

nonn,easy

Author

R. J. Mathar, Jun 11 2019

Status

approved