OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..2500 (terms 1..200 from T. D. Noe)
Martin Burtscher, Igor Szczyrba, Rafał Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.
C. A. Charalambides, Lucas numbers and polynomials of order k and the length of the longest circular success run, The Fibonacci Quarterly, 29 (1991), 290-297.
Tony D. Noe and Jonathan Vos Post, Primes in Fibonacci n-step and Lucas n-step Sequences, J. of Integer Sequences, Vol. 8 (2005), Article 05.4.4.
Eric Weisstein's World of Mathematics, Lucas 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 > 0, a(0)=9, a(n)=-1 for n=-8..-1
G.f.: -x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7 + 9*x^8) / ( -1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 ). - R. J. Mathar, Jun 20 2011
a(n) = n*Sum_{k=1..n} (Sum_{i=0..floor((n-k)/9)} (-1)^i*binomial(k, k-i)*binomial(n-9*i-1, k-1))/k. - Vladimir Kruchinin, Aug 10 2011
MATHEMATICA
a={-1, -1, -1, -1, -1, -1, -1, -1, 9}; Table[s=Plus@@a; a=RotateLeft[a]; a[[ -1]]=s, {n, 50}]
PROG
(Maxima)
a(n):=n*sum(sum((-1)^i*binomial(k, k-i)*binomial(n-9*i-1, k-1), i, 0, (n-k)/9)/k, k, 1, n);
makelist(a(n), n, 1, 17); /* Vladimir Kruchinin, Aug 10 2011 */
(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-1)*[1; 3; 7; 15; 31; 63; 127; 255; 511])[1, 1] \\ Charles R Greathouse IV, Jun 15 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, Apr 22 2005
STATUS
approved