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In general, a first order inhomogeneous recurrence of the form s(0) = a, s(n)= m*s(n-1) + k, n>0, will have a closed form of a*m^n +((m^n-1)/(m=-1))*k. - Gary Detlefs, Jun 07 2024
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1, 5, 17, 53, 161, 485, 1457, 4373, 13121, 39365, 118097, 354293, 1062881, 3188645, 9565937, 28697813, 86093441, 258280325, 774840977, 2324522933, 6973568801, 20920706405, 62762119217, 188286357653, 564859072961, 1694577218885, 5083731656657, 15251194969973
g:=x* ((1+x)/(1-3*x)/(1-x)): gser:=series(g, x=0, 43): seq(coeff(gser, x, n), n=10..30); # Zerinvary Lajos, Jan 11 2009; typo fixed by Marko Mihaily, Mar 07 2009
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G.f.:(1+x)/((1-3*x)(1-x)). - Zerinvary Lajos, Jan 11 2009, _; corrected by _R. J. Mathar_, Jan 21 2009
g:=x*((1+x)/(1-3*x)/(1-x)): gser:=series(g, x=0, 43): seq(coeff(gser, x, n), n=1..30); # Zerinvary Lajos, Jan 11 2009; typo fixed by Marko Mihaily, Mar 07 2009
Divided g.f. by x to match the offset - R. J. Mathar, Jan 21 2009
Typo in Maple program fixed by Marko Mihaily, Mar 07 2009
C. Creighton Dement, <a href="http://mathforum.org/kb/thread.jspa?forumID=13&threadID=1962419">A paper on floretions and quaternions, some questions</a>, The Math Forum.
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