A175899 - OEIS

%I #28 Feb 01 2018 03:43:06

%S 0,2,3,10,5,17,21,42,48,97,132,229,325,555,818,1338,2023,3266,4997,

%T 7965,12309,19494,30268,47733,74380,116989,182649,286835,448398,

%U 703462,1100531,1725530,2700789,4232985,6627381,10384834,16261944,25478185,39901540,62509797

%N a(n) = a(n-2) + a(n-3) + 2*a(n-4), with a(1) = 0, a(2) = 2, a(3) = 3, a(4) = 10.

%C According to the reference, p divides a(p) for every prime p.

%H Reinhard Zumkeller, <a href="/A175899/b175899.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Pite, <a href="http://www.jstor.org/stable/10.4169/002557010x521877">Problem 1851</a>, Mathematics Magazine 83 (2010) 303.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 2).

%F 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

%F 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

%p a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <2|1|1|0>>^n.

%p         <<4,0,2,3>>)[1, 1]:

%p seq(a(n), n=1..50);  # _Alois P. Heinz_, Oct 21 2011

%t LinearRecurrence[{0,1,1,2},{0,2,3,10},40] (* _Harvey P. Dale_, Jul 24 2011 *)

%o (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 */

%o (Haskell)

%o a175899 n = a175899_list !! (n-1)

%o a175899_list = 0 : 2 : 3 : 10 : zipWith (+) (map (* 2) a175899_list)

%o    (zipWith (+) (tail a175899_list) (drop 2 a175899_list))

%o -- _Reinhard Zumkeller_, Mar 23 2012

%Y Cf. A001608, A001634.

%K nonn,easy

%O 1,2

%A _John W. Layman_, Oct 11 2010