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 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 (list; graph; refs; listen; history; text; internal format)
 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 Index entries for linear recurrences with constant coefficients, signature (1,3,1). FORMULA a(n) + a(n+1) = A048655(n). 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; G.f. -x*(1+3*x) / ( (1+x)*(x^2+2*x-1) ). - 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: A296663 A066345 A026570 * A244791 A220004 A255512 Adjacent sequences:  A111952 A111953 A111954 * A111956 A111957 A111958 KEYWORD easy,nonn AUTHOR Creighton Dement, Aug 25 2005 STATUS approved

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Last modified June 22 04:06 EDT 2021. Contains 345367 sequences. (Running on oeis4.)