A122602 a(1) = 1; a(2) = 0; a(3) = 0; a(4) = 0; a(5) = 0; a(6) = 0; a(7) = 0; a(8) = 0; a(9) = 0; a(10) = 0; a(n) = a(n - 1) + 9a(n - 2) - 8a(n - 3) - 28a(n - 4) + 21a(n - 5) + 35a(n - 6) - 20a(n - 7) - 15a(n - 8) + 5a(n - 9) + a(n - 10) for n >= 11.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 11, 65, 77, 350, 440, 1700, 2244, 7752, 10659, 33915, 48279, 144210, 211508, 600875, 904475, 2466750, 3798795, 10015005, 15737864, 40320149, 64512209, 161280568, 262255753, 641885440, 1059105390, 2544612396

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 20 2006

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (1, 9, -8, -28, 21, 35, -20, -15, 5, 1).

Crossrefs

Cf. A066170.

Programs

Maple

a[1]:=1: a[2]:=0: a[3]:=0: a[4]:=0: a[5]:=0: a[6]:=0: a[7]:=0: a[8]:=0: a[9]:=0: a[10]:=0: for n from 11 to 39 do a[n]:=a[n-1]+9*a[n-2]-8*a[n-3]-28*a[n-4]+21*a[n-5]+35*a[n-6]-20*a[n-7]-15*a[n-8]+5*a[n-9]+a[n-10] od: seq(a[n],n=1..39);

Mathematica

M = {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 5, -15, -20, 35, 21, -28, -8, 9, 1}}; v[1] = {1, 0, 0, 0, 0, 0, 0, 0, 0, 0}; v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
LinearRecurrence[{1,9,-8,-28,21,35,-20,-15,5,1},{1,0,0,0,0,0,0,0,0,0},50] (* Harvey P. Dale, Dec 03 2014 *)

Formula

G.f.:((5*x^4-5*x^2+1)*(x^5-3*x^4-3*x^3+4*x^2+x-1))/((x-1)*(x^3-2*x^2-x+1)*(x^6+8*x^5+8*x^4-6*x^3-6*x^2+x+1)). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009]

Extensions

Edited by N. J. A. Sloane, Oct 08 2006