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 A012855 a(0) = 0, a(1) = 1, a(2) = 1; thereafter a(n) = 5*a(n-1) - 4*a(n-2) + a(n-3). 7
 0, 1, 1, 1, 2, 7, 28, 114, 465, 1897, 7739, 31572, 128801, 525456, 2143648, 8745217, 35676949, 145547525, 593775046, 2422362079, 9882257736, 40315615410, 164471408185, 670976837021, 2737314167775, 11167134898976 (list; graph; refs; listen; history; text; internal format)
 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 a(n) = 1 + A176476(n-3) = 1 + Sum_{k=0..n-3} A000931(5*k+2) for n >= 3. - Jianing Song, Feb 04 2019 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 Cf. A000931, A012814, A012864, A060006, A176476. Sequence in context: A068944 A215143 A289158 * A224066 A150646 A128611 Adjacent sequences:  A012852 A012853 A012854 * A012856 A012857 A012858 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

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Last modified May 18 21:30 EDT 2021. Contains 344003 sequences. (Running on oeis4.)