A220699 a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-4)*a(n-2) + 1.

0, 0, 1, 2, 3, 6, 13, 32, 85, 246, 757, 2480, 8537, 30858, 116229, 455668, 1850417, 7774102, 33679941, 150291472, 689170529, 3244125554, 15649195077, 77287580604, 390271482145, 2013310674830, 10599283282021

Offset: 0

Author

Vincenzo Librandi, Dec 25 2012

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..800

Crossrefs

Cf. A185108, A185109, A185308, A185309, A186738, A186739, A213720, A187830.

Programs

Magma

[n le 2 select 0 else Self(n-1)+(n-5)*Self(n-2) + 1: n in [1..30]];

Mathematica

RecurrenceTable[{a[1]==0, a[2]==0, a[n]==a[n-1] + (n-5) a[n-2] + 1}, a, {n, 40}]

Formula

a(0)=a(1)=0, a(2)=1, a(n) = 2*a(n-1)+(n-5)*a(n-2)-(n-5)*a(n-3).

a(n) ~ (sqrt(Pi)/2+sqrt(2)) * n^(n/2-3/2)*exp(sqrt(n)-n/2-1/4) * (1-29/(24*sqrt(n))). - Vaclav Kotesovec, Dec 27 2012