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A228644
Expansion of g.f. 1/ (1-x^1*(1-x^(m+1))/ (1-x^2*(1-x^(m+2))/ (1- ... ))) for m=7.
7
1, 1, 1, 2, 3, 5, 9, 15, 26, 44, 76, 131, 225, 389, 670, 1156, 1994, 3439, 5934, 10236, 17661, 30470, 52569, 90699, 156483, 269985, 465811, 803677, 1386609, 2392357, 4127611, 7121498, 12286951, 21199078, 36575462, 63104849, 108876873, 187848862, 324101847
OFFSET
0,4
LINKS
Paul D. Hanna et al., Formula Needed for a Family of Continued Fractions and follow-up messages on the SeqFan list, Jul 28 2013
Index entries for linear recurrences with constant coefficients, signature (1,1,1,0,0,-1,-1,-3,-2,-1,0,2,2,3,3,1,0,0,-2,-1,-1,-1).
FORMULA
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)).
MAPLE
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);
MATHEMATICA
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 *)
CROSSREFS
Cf. A143064 (m=0), A227360 (m=2), A173173 (m=3), A227374 (m=4), A227375 (m=5), A228646(m=6), A228645 (m=9).
Column m=7 of A185646.
Sequence in context: A220127 A286887 A018157 * A003065 A239909 A185648
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 28 2013
STATUS
approved