OFFSET
0,5
COMMENTS
Old name was "Take every 5th term of Padovan sequence A000931".
Lim_{n -> infinity} a(n+1)/a(n) = p^5 = 4.0795956..., where p is the plastic constant (A060006). - Jianing Song, Feb 04 2019
LINKS
Index entries for linear recurrences with constant coefficients, signature (5, -4, 1).
FORMULA
a(n) = A000931(5*n-12) for n >= 3. - Alois P. Heinz, Feb 04 2019
G.f. (4x^2 - x)/(x^3 - 4x^2 + 5x - 1). For n > 2, a(n) = 1 + Sum_{k=0..n-3} A012814(k). - Ralf Stephan, Jan 15 2004
MAPLE
A012855 := proc(n, A, B, C) option remember; if n = 0 then A elif n = 1 then B elif n = 2 then C else 5*procname(n-1, A, B, C)-4*procname(n-2, A, B, C)+procname(n-3, A, B, C); fi; end; [ seq(A012855(i, 0, 1, 1), i = 0..40) ]; # R. J. Mathar, Dec 30 2011
MATHEMATICA
CoefficientList[Series[(4x^2-x)/(x^3-4x^2+5x-1), {x, 0, 40}], x] (* or *) LinearRecurrence[{5, -4, 1}, {0, 1, 1}, 40] (* Harvey P. Dale, Mar 28 2013 *)
PROG
(PARI) a(n) = my(v=vector(n+1), u=[0, 1, 1]); for(k=1, n+1, v[k]=if(k<=3, u[k], 5*v[k-1] - 4*v[k-2] + v[k-3])); v[n+1] \\ Jianing Song, Feb 04 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Feb 06 2019 at the suggestion of Jianing Song, replacing imprecise definition with formula from Harvey P. Dale, Mar 28 2013
STATUS
approved