A177794 G.f. A satisfies -x+(1+x^3-x)*A+(x^4-x^2)*A^2+(x^5-x^3)*A^3-x^4*A^4 = 0.

1, 1, 1, 1, 2, 4, 8, 16, 33, 69, 145, 306, 651, 1398, 3026, 6590, 14425, 31720, 70040, 155229, 345193, 770002, 1722487, 3863274, 8685608, 19570860, 44188976, 99965361, 226548082, 514275345, 1169255837, 2662319778, 6070294053, 13858727891, 31678845485

Offset

1,5

Comments

Used in the enumeration of prudent self-avoiding walks.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

S. Gao, H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, (submitted to INTEGERS: The Electronic Journal of Combinatorial Number Theory).

Mathematica

m = 36; A[_] = 0;
Do[A[x_] = (x + A[x]^2*x^2 + A[x]^3*x^3 + A[x]^2*(-1 + A[x]^2)*x^4 - A[x]^3*x^5)/(1 - x + x^3) + O[x]^m, {m}];
CoefficientList[A[x]/x, x] (* Jean-François Alcover, Oct 03 2019 *)

Prog

(PARI) /* verification */
V177794=[1, 1, 1, 1, 2, 4, 8, 16, 33, 69, 145];
A=x*Ser(V177794); /*  = x + x^2 + x^3 + x^4 + 2*x^5 + 4*x^6 + 8*x^7 + ... */
-x+(1+x^3-x)*A+(x^4-x^2)*A^2+(x^5-x^3)*A^3-x^4*A^4 /* = O(x^12) = "zero" */
/* Joerg Arndt, May 14 2011 */

Crossrefs

Cf. A178035.

Sequence in context: A367715 A126683 A005821 * A004149 A129986 A368461

Adjacent sequences: A177791 A177792 A177793 * A177795 A177796 A177797

Keyword

nonn

Author

This sequence was derived by Dr. Aaron Meyerowitz and submitted by Shanzhen Gao, May 13 2010

Status

approved