|
%I #16 Feb 06 2019 12:59:45
%S 1,6,136,2016,32896,523776,8390656,134209536,2147516416,34359607296,
%T 549756338176,8796090925056,140737496743936,2251799780130816,
%U 36028797153181696,576460751766552576,9223372039002259456
%N a(n) = Sum_{k = 0..n} C(4*n + 1, 4*k).
%H Harvey P. Dale, <a href="/A090407/b090407.txt">Table of n, a(n) for n = 0..800</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,64).
%F From _Harvey P. Dale_, Jan 19 2012: (Start)
%F a(0) = 1, a(1) = 6, a(n) = 12*a(n-1)+64*a(n-2).
%F G.f.: (6*x-1)/(64*x^2+12*x-1). (End)
%F a(n) = (1/2) * 4^n * (4^n + (-1)^n). - _Peter Bala_, Feb 06 2019
%t Table[Sum[Binomial[4n+1,4k],{k,0,n}],{n,0,30}] (* or *) LinearRecurrence[ {12,64},{1,6},30] (* _Harvey P. Dale_, Jan 19 2012 *)
%Y Cf. A070775, A001025, A090408, A038503.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 29 2003
|
