|
%I #17 Jun 17 2020 07:01:10
%S 1,1,4,12,37,114,351,1081,3329,10252,31572,97229,299426,922111,
%T 2839729,8745217,26931732,82938844,255418101,786584466,2422362079,
%U 7459895657,22973462017,70748973084,217878227876,670976837021,2066337330754
%N Quadrisection of a Padovan sequence.
%C Quadrisection of sequence with g.f. 1/(1-x^2-x^3), or A000931(n+3).
%H Harvey P. Dale, <a href="/A099098/b099098.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,1).
%F G.f.: (1-x-x^2)/(1-2x-3x^2-x^3);
%F a(n)=sum{k=0..2n, binomial(k, 4n-2k)};
%F a(n)=2a(n-1)+3a(n-2)+a(n-3);
%F a(n)=A000931(4n+3).
%F a(n) = Sum [k=0..n, C(2n-k, 2k) ].
%e 1 + x + 4*x^2 + 12*x^3 + 37*x^4 + 114*x^5 + 351*x^6 + ...
%t LinearRecurrence[{2,3,1},{1,1,4},40] (* _Harvey P. Dale_, Aug 23 2011 *)
%Y Bisection of A005251.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Sep 29 2004
|
