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%I #24 Jul 01 2023 15:55:16
%S 1,1,1,2,3,5,9,15,26,44,76,131,225,389,670,1156,1994,3439,5934,10236,
%T 17661,30470,52569,90699,156483,269985,465811,803677,1386609,2392357,
%U 4127611,7121498,12286951,21199078,36575462,63104849,108876873,187848862,324101847
%N Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=7.
%H Alois P. Heinz, <a href="/A228644/b228644.txt">Table of n, a(n) for n = 0..1000</a>
%H Paul D. Hanna et al., <a href="http://list.seqfan.eu/oldermail/seqfan/2013-July/011445.html">Formula Needed for a Family of Continued Fractions</a> and follow-up messages on the SeqFan list, Jul 28 2013
%H <a href="/index/Rec#order_22">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,1,0,0,-1,-1,-3,-2,-1,0,2,2,3,3,1,0,0,-2,-1,-1,-1).
%F G.f.: -(x^18 +x^17 +x^16 +2*x^15 +x^14 -2*x^11 -2*x^10 -2*x^9 -2*x^8 +x^5 +x^4 +x^3 +x^2-1) / ((x-1)*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)*(x^15 +x^14 +x^13 +2*x^12 -x^9 -2*x^8 -2*x^7 -x^6 +x^3 +x^2 +x-1)).
%p a:= n-> coeff(series(-(x^18 +x^17 +x^16 +2*x^15 +x^14 -2*x^11 -2*x^10 -2*x^9 -2*x^8 +x^5 +x^4 +x^3 +x^2-1) / ((x-1)*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)*(x^15 +x^14 +x^13 +2*x^12 -x^9 -2*x^8 -2*x^7 -x^6 +x^3 +x^2 +x-1)), x, n+1), x, n): seq(a(n), n=0..50);
%t nMax = 39; col[m_ /; 0 <= m <= nMax] := 1/(1 + ContinuedFractionK[-x^k (1 - x^(m + k)), 1, {k, 1, Ceiling[nMax/2]}]) + O[x]^(2 nMax) // CoefficientList[#, x]&; A228644 = col[7][[1 ;; nMax]] (* _Jean-François Alcover_, Nov 03 2016 *)
%Y Cf. A143064 (m=0), A227360 (m=2), A173173 (m=3), A227374 (m=4), A227375 (m=5), A228646(m=6), A228645 (m=9).
%Y Column m=7 of A185646.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Aug 28 2013
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