login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A025251
a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-3)*a(3) for n >= 4.
1
0, 1, 2, 0, 2, 4, 2, 12, 18, 24, 82, 120, 242, 620, 1010, 2324, 5154, 9520, 22178, 46512, 94178, 214548, 446690, 952732, 2122034, 4475592, 9776626, 21491496, 46096338, 101585276, 222360530, 483573796, 1068438594, 2341596256, 5140674882, 11369018464
OFFSET
1,3
FORMULA
G.f.: (1+x^2-sqrt(1-2*x^2-8*x^3+x^4))/2. - Michael Somos, Jun 08 2000
Conjecture: n*(n^2+n+1)*a(n) +(n-1)*(n^2+2*n+3)*a(n-1) -2*(n-3)*(n^2+n+1)*a(n-2) +2*(-5*n^3+16*n^2+19*n+30)*a(n-3) +(-7*n^3+23*n^2+59*n+126)*a(n-4) +(n-7)*(n^2+2*n+3)*a(n-5)=0. - R. J. Mathar, Feb 25 2015
PROG
(PARI) a(n)=polcoeff((x^2-sqrt(1-2*x^2-8*x^3+x^4+x*O(x^n)))/2, n)
CROSSREFS
Sequence in context: A291956 A023987 A021498 * A193334 A185081 A011119
KEYWORD
nonn
STATUS
approved