OFFSET
1,2
COMMENTS
According to the reference, p divides a(p) for every prime p.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Pite, Problem 1851, Mathematics Magazine 83 (2010) 303.
Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 2).
FORMULA
G.f.: x*(-2*x-3*x^2-8*x^3)/(-1+x^2+x^3+2*x^4). - Harvey P. Dale, Jul 24 2011
a(n) = n*sum(k=1..n/2, sum(j=0..k, binomial(j,n-4*k+2*j)*2^(k-j) * binomial(k,j))/k), n>0. - Vladimir Kruchinin, Oct 21 2011
MAPLE
a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <2|1|1|0>>^n.
<<4, 0, 2, 3>>)[1, 1]:
seq(a(n), n=1..50); # Alois P. Heinz, Oct 21 2011
MATHEMATICA
LinearRecurrence[{0, 1, 1, 2}, {0, 2, 3, 10}, 40] (* Harvey P. Dale, Jul 24 2011 *)
PROG
(Maxima) a(n):=n*sum(sum(binomial(j, n-4*k+2*j)*2^(k-j)*binomial(k, j), j, 0, k)/k, k, 1, n/2); /* Vladimir Kruchinin, Oct 21 2011 */
(Haskell)
a175899 n = a175899_list !! (n-1)
a175899_list = 0 : 2 : 3 : 10 : zipWith (+) (map (* 2) a175899_list)
(zipWith (+) (tail a175899_list) (drop 2 a175899_list))
-- Reinhard Zumkeller, Mar 23 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
John W. Layman, Oct 11 2010
STATUS
approved