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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

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(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: 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

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Last modified November 18 19:06 EST 2017. Contains 294894 sequences.