OFFSET
5,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 5..5000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Chai Wah Wu, Dec 29 2016: (Start)
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 11.
G.f.: x^5*(1 + 41*x -123*x^2 + 149*x^3 - 93*x^4 + 30*x^5 - 4*x^6)/(1-x)^6. (End)
From G. C. Greubel, Jan 22 2020: (Start)
a(n) = (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120, for n>5, with a(5) = 1.
E.g.f.: (-480 -720*x -180*x^2 +60*x^3 +30*x^4 -4*x^5 + (480 +240*x -300*x^2 + 40*x^3 +20*x^4 +x^5)*exp(x))/120. (End)
MAPLE
seq( `if`(n=5, 1, (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120), n=5..50); # G. C. Greubel, Jan 22 2020
MATHEMATICA
Join[{1, 47, 144, 328, 640}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1131, 1863, 2910, 4359, 6311, 8882}, 5004]] (* Vincenzo Librandi, Dec 30 2016 *)
Table[If[n==5, 1, (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120], {n, 5, 50}] (* G. C. Greubel, Jan 22 2020 *)
PROG
(Magma) I:=[1, 47, 144, 328, 640, 1131, 1863, 2910, 4359, 6311, 8882]; [n le 11 select I[n] else 6*Self(n-1)-15*Self(n-2) +20*Self(n-3)-15*Self(n-4)+6*Self(n-5)-Self(n-6): n in [1..50]]; // Vincenzo Librandi, Dec 30 2016
(PARI) vector(45, n, my(m=n+4); if(m==5, 1, (480 +524*m -250*m^2 -45*m^3 +10*m^4 +m^5)/120)) \\ G. C. Greubel, Jan 22 2020
(Sage) [1]+[(480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120 for n in (6..50)] # G. C. Greubel, Jan 22 2020
(GAP) Concatenation([1], List([6..50], n-> (480 +524*n -250*n^2 -45*n^3 +10*n^4 +n^5)/120 )); # G. C. Greubel, Jan 22 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 28 2000
STATUS
approved