|
%I #11 Jan 02 2022 17:32:26
%S 1,1,1,1,3,11,31,71,145,289,601,1321,2979,6683,14743,32111,69697,
%T 151777,332113,728689,1598883,3503627,7668079,16774775,36704017,
%U 80343361,175916521,385196761,843365379,1846290395,4041672871,8847607391
%N a(n) = Sum_{k=0..n} C(n,4k)*2^k.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,1).
%F G.f.: (1-x)^3/((1-x)^4-2*x^4);
%F a(n) = Sum_{k=0..floor(n/2)} binomial(n,4*k)*2^k;
%F a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)+a(n-4).
%t Table[Sum[Binomial[n,4k]2^k,{k,0,n}],{n,0,40}] (* or *) LinearRecurrence[ {4,-6,4,1},{1,1,1,1},40] (* _Harvey P. Dale_, Feb 26 2012 *)
%Y Cf. A093406.
%K easy,nonn
%O 0,5
%A _Paul Barry_, Jul 23 2004
|
