A193418 Expansion of x*(x^2+x-1)/(3*x^6-4*x^5+x^4-3*x^2+4*x-1).

1, 3, 8, 23, 69, 206, 616, 1846, 5537, 16609, 49824, 149469, 448405, 1345212, 4035632, 12106892, 36320673, 108962015, 326886040, 980658115, 2941974341, 8825923018, 26477769048, 79433307138, 238299921409, 714899764221, 2144699292656

Offset: 1

Author

Yalcin Aktar, Jul 26 2011

Keywords

• nonn

Comments

Conjecture: log(A005960-a(n)) ~ (log(2)*(2*n-11)).

Crossrefs

Cf. A005960.

Formula

a(n) = b(n+1,3)-b(n+1,4) with b(n,c) = sum(floor(3^m/2^c), m=1..n).

G.f.: x*(x^2+x-1) / (3*x^6-4*x^5+x^4-3*x^2+4*x-1).

a(n) = (9*3^n+4*n+1-(1+(-1)^n)*(1+4*i^n))/32, where i=sqrt(-1). - Bruno Berselli, Jul 30 2011