OFFSET
1,1
COMMENTS
Sums of all distinct products of 3 out of 5 consecutive integers, starting with the n-th integer; value of 3rd elementary symmetric function on the 5 consecutive integers. cf. Vieta's formulas.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = 5*(n+3)*(2*n^2+12*n+15). G.f.: 5*x*(116-229*x+170*x^2-45*x^3)/(1-x)^4. [Colin Barker, Mar 28 2012]
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Vincenzo Librandi, Jun 28 2012
MATHEMATICA
r = {}; k = 0; a = {}; Do[Do[Do[If[(d != b) && (d != c) && (b != c), AppendTo[a, {d, b, c}]], {c, b, 5}], {b, d, 5}], {d, 1, 5}]; Do[Do[k = k + Sum[(x + a[[v, 1]]) (x + a[[v, 2]]) (x + a[[v, 3]]), {v, 1, Length[a]}]]; AppendTo[r, k]; k = 0, {x, 1, 50}]; r
CoefficientList[Series[5*(116-229*x+170*x^2-45*x^3)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Jun 28 2012 *)
PROG
(Magma) I:=[580, 1175, 2070, 3325]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 28 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Jan 23 2007
STATUS
approved