%I
%S 0,1,4,7,20,45,112,267,648,1561,3772,9103,21980,53061,128104,309267,
%T 746640,1802545,4351732,10506007,25363748,61233501,147830752,
%U 356895003,861620760,2080136521,5021893804,12123924127,29269742060,70663408245
%N a(n) = A078343(n) + (1)^n.
%C This sequence is a companion sequence to A111954 (compare formula / program code). Three other companion sequences (i.e., they are generated by the same floretion given in the program code) are A105635, A097076 and A100828.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,1).
%F a(n) + a(n+1) = A048655(n).
%F a(n) = a(n1) + 3*a(n2) + a(n3), n >= 3; a(n) = (1/4*sqrt(2)+1)*(1sqrt(2))^n + (1/4*sqrt(2)+1)*(1+sqrt(2))^n  (1)^n;
%F G.f. x*(1+3*x) / ( (1+x)*(x^2+2*x1) ).  _R. J. Mathar_, Oct 02 2012
%t LinearRecurrence[{1,3,1},{0,1,4},40] (* _Harvey P. Dale_, Mar 12 2015 *)
%o Floretion Algebra Multiplication Program, FAMP Code: 4kbasejseq[J*D] with J =  .25'i + .25'j + .5'k  .25i' + .25j' + .5k'  .5'kk'  .25'ik'  .25'jk'  .25'ki'  .25'kj'  .5e and D = + .5'i  .25'j + .25'k + .5i'  .25j' + .25k'  .5'ii'  .25'ij'  .25'ik'  .25'ji'  .25'ki'  .5e. (an initial term 0 was added to the sequence)
%Y Cf. A078343, A000129, A001333, A111954, A111956, A007070, A077995, A100828, A097076, A105635.
%K easy,nonn
%O 0,3
%A _Creighton Dement_, Aug 25 2005
