login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A111955 a(n) = A078343(n) + (-1)^n. 2

%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(n-1) + 3*a(n-2) + a(n-3), n >= 3; a(n) = (-1/4*sqrt(2)+1)*(1-sqrt(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*x-1) ). - _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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 22:20 EDT 2021. Contains 346265 sequences. (Running on oeis4.)