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
Keywords
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).
Crossrefs
Cf. A178035.
Programs
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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 *) -
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 */
Comments