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 A104144 a(n) = Sum_{k=1..9} a(n-k); a(8) = 1, a(n) = 0 for n < 8. 18
 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2040, 4076, 8144, 16272, 32512, 64960, 129792, 259328, 518145, 1035269, 2068498, 4132920, 8257696, 16499120, 32965728, 65866496, 131603200, 262947072, 525375999, 1049716729, 2097364960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS Sometimes called the Fibonacci 9-step numbers. For n >= 8, this gives the number of integers written without 0 in base ten, the sum of digits of which is equal to n-7. E.g., a(11) = 8 because we have the 8 numbers: 4, 13, 22, 31, 112, 121, 211, 1111. The offset for this sequence is fairly arbitrary. - N. J. A. Sloane, Feb 27 2009 LINKS T. D. Noe, Table of n, a(n) for n = 0..208 Martin Burtscher, Igor Szczyrba, RafaĆ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5. Eric Weisstein's World of Mathematics, Fibonacci n-Step Number Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,1,1,1,1,1). FORMULA a(n) = Sum_{k=1..9} a(n-k) for n > 8, a(8) = 1, a(n) = 0 for n=0..7. G.f.: x^8/(1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9). - N. J. A. Sloane, Dec 04 2011 Another form of the g.f. f: f(z)=(z^8-z^9)/(1-2*z+z^(10)), then a(n)=sum((-1)^i*binomial(n-8-9*i,i)*2^(n-8-10*i),i=0..floor((n-8)/10))-sum((-1)^i*binomial(n-9-9*i,i)*2^(n-9-10*i),i=0..floor((n-9)/10)) with sum(alpha(i),i=m..n)=0 for m>n. - Richard Choulet, Feb 22 2010 From N. J. A. Sloane, Dec 04 2011: (Start) Let b be the smallest root (in magnitude) of g(x) := 1-x-x^2-x^3-x^4-x^5-x^6-x^7-x^8-x^9), b = 0.50049311828655225605926845999420216157202861343888... Let c = -b^8/g'(b) = 0.00099310812055463178382193226558248643030626601288701... Then a(n) is the nearest integer to c/b^n. (End) MAPLE for n from 0 to 50 do k(n):=sum((-1)^i*binomial(n-8-9*i, i)*2^(n-8-10*i), i=0..floor((n-8)/10))-sum((-1)^i*binomial(n-9-9*i, i)*2^(n-9-10*i), i=0..floor((n-9)/10)):od:seq(k(n), n=0..50); a:=taylor((z^8-z^9)/(1-2*z+z^(10)), z=0, 51); for p from 0 to 50 do j(p):=coeff(a, z, p):od :seq(j(p), p=0..50); # Richard Choulet, Feb 22 2010 MATHEMATICA a={1, 0, 0, 0, 0, 0, 0, 0, 0}; Table[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s, {n, 50}] LinearRecurrence[{1, 1, 1, 1, 1, 1, 1, 1, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 1}, 50] (* Vladimir Joseph Stephan Orlovsky, May 25 2011 *) With[{nn=9}, LinearRecurrence[Table[1, {nn}], Join[Table[0, {nn-1}], {1}], 50]] (* Harvey P. Dale, Aug 17 2013 *) PROG (PARI) a(n)=([0, 1, 0, 0, 0, 0, 0, 0, 0; 0, 0, 1, 0, 0, 0, 0, 0, 0; 0, 0, 0, 1, 0, 0, 0, 0, 0; 0, 0, 0, 0, 1, 0, 0, 0, 0; 0, 0, 0, 0, 0, 1, 0, 0, 0; 0, 0, 0, 0, 0, 0, 1, 0, 0; 0, 0, 0, 0, 0, 0, 0, 1, 0; 0, 0, 0, 0, 0, 0, 0, 0, 1; 1, 1, 1, 1, 1, 1, 1, 1, 1]^n*[0; 0; 0; 0; 0; 0; 0; 0; 1])[1, 1] \\ Charles R Greathouse IV, Jun 16 2015 (PARI) A104144(n, m=9)=(matrix(m, m, i, j, j==i+1||i==m)^n)[1, m] \\ M. F. Hasler, Apr 22 2018 CROSSREFS Cf. A000045, A000073, A000078, A001591, A001592, A066178, A079262 (Fibonacci n-step numbers). Cf. A255529 (Indices of primes in this sequence). Sequence in context: A145115 A172318 A234590 * A258800 A194632 A282584 Adjacent sequences:  A104141 A104142 A104143 * A104145 A104146 A104147 KEYWORD nonn,easy AUTHOR Jean Lefort (jlefort.apmep(AT)wanadoo.fr), Mar 07 2005 EXTENSIONS Edited by N. J. A. Sloane, Aug 15 2006 and Nov 11 2006 Incorrect formula deleted by N. J. A. Sloane, Dec 04 2011 Name edited by M. F. Hasler, Apr 22 2018 STATUS approved

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Last modified October 19 20:55 EDT 2019. Contains 328224 sequences. (Running on oeis4.)