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 A017898 Expansion of (1-x)/(1-x-x^4). 17
 1, 0, 0, 0, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 36, 50, 69, 95, 131, 181, 250, 345, 476, 657, 907, 1252, 1728, 2385, 3292, 4544, 6272, 8657, 11949, 16493, 22765, 31422, 43371, 59864, 82629, 114051, 157422, 217286, 299915, 413966, 571388, 788674 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS A LamÃ© sequence of higher order. Essentially the same as A003269, which has much more information. Number of compositions of n into parts >= 4. - Joerg Arndt, Aug 13 2012 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Christian Ballot, On Functions Expressible as Words on a Pair of Beatty Sequences, Journal of Integer Sequences, Vol. 20 (2017), Article 17.4.2. I. M. Gessel, Ji Li, Compositions and Fibonacci identities, J. Int. Seq. 16 (2013) 13.4.5 J. Hermes, Anzahl der Zerlegungen einer ganzen rationalen Zahl in Summanden, Math. Ann., 45 (1894), 371-380. Milan Janjic, Binomial Coefficients and Enumeration of Restricted Words, Journal of Integer Sequences, 2016, Vol 19, #16.7.3 T. Mansour, M. Shattuck, A monotonicity property for generalized Fibonacci sequences, arXiv:1410.6943 [math.CO], 2014. J. D. Opdyke, A unified approach to algorithms generating unrestricted.., J. Math. Model. Algor. 9 (2010) 53-97 Index entries for linear recurrences with constant coefficients, signature (1,0,0,1). FORMULA a(n) = a(n-1) + a(n-4). - R. J. Mathar, Mar 06 2008 G.f.: 1/(1-sum(k>=4, x^k)). - Joerg Arndt, Aug 13 2012 Apparently a(n) = hypergeometric([1-1/4*n, 5/4-1/4*n, 3/2-1/4*n, 7/4-1/4*n],[4/3-1/3*n, 5/3-1/3*n, 2-1/3*n], -4^4/3^3) for n>=13. - Peter Luschny, Sep 18 2014 a(n) = A003269(n+1)-A003269(n). - R. J. Mathar, Jun 10 2018 MAPLE f := proc(r) local t1, i; t1 := []; for i from 1 to r do t1 := [op(t1), 0]; od: for i from 1 to r+1 do t1 := [op(t1), 1]; od: for i from 2*r+2 to 50 do t1 := [op(t1), t1[i-1]+t1[i-1-r]]; od: t1; end; # set r = order a:= n-> (Matrix(4, (i, j)-> if (i=j-1) then 1 elif j=1 then [1, 0\$2, 1][i] else 0 fi)^n)[4, 4]: seq(a(n), n=0..42); # Alois P. Heinz, Aug 04 2008 MATHEMATICA LinearRecurrence[{1, 0, 0, 1}, {1, 0, 0, 0}, 80] (* Vladimir Joseph Stephan Orlovsky, Feb 11 2012 *) PROG (PARI) a(n)=([0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1; 1, 0, 0, 1]^n*[1; 0; 0; 0])[1, 1] \\ Charles R Greathouse IV, Oct 03 2016 CROSSREFS For LamÃ© sequences of orders 1 through 9 see A000045, A000930, this one, and A017899-A017904. Sequence in context: A238874 A099559 A247084 * A003269 A087221 A295072 Adjacent sequences:  A017895 A017896 A017897 * A017899 A017900 A017901 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 25 22:57 EDT 2018. Contains 315425 sequences. (Running on oeis4.)