

A111955


a(n) = A078343(n) + (1)^n.


2



0, 1, 4, 7, 20, 45, 112, 267, 648, 1561, 3772, 9103, 21980, 53061, 128104, 309267, 746640, 1802545, 4351732, 10506007, 25363748, 61233501, 147830752, 356895003, 861620760, 2080136521, 5021893804, 12123924127, 29269742060, 70663408245
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OFFSET

0,3


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..29.
Index entries for linear recurrences with constant coefficients, signature (1,3,1).


FORMULA

a(n) + a(n+1) = A048655(n).
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;
G.f. x*(1+3*x) / ( (1+x)*(x^2+2*x1) ).  R. J. Mathar, Oct 02 2012


MATHEMATICA

LinearRecurrence[{1, 3, 1}, {0, 1, 4}, 40] (* Harvey P. Dale, Mar 12 2015 *)


PROG

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)


CROSSREFS

Cf. A078343, A000129, A001333, A111954, A111956, A007070, A077995, A100828, A097076, A105635.
Sequence in context: A266822 A066345 A026570 * A244791 A220004 A255512
Adjacent sequences: A111952 A111953 A111954 * A111956 A111957 A111958


KEYWORD

easy,nonn


AUTHOR

Creighton Dement, Aug 25 2005


STATUS

approved



