OFFSET
1,1
COMMENTS
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = ((n^5 + (n+1)^5 + (n+2)^5 + (n+3)^5 + (n+4)^5) /5) /5.
From Colin Barker, Sep 18 2017: (Start)
G.f.: x*(177 - 574*x + 886*x^2 - 714*x^3 + 301*x^4 - 52*x^5) / (1 - x)^6.
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>6.
(End)
EXAMPLE
a(1) = (1^5 + 2^5 + 3^5 + 4^5 +5^5)/25 = (1+32+243+1024+3125)/25 = 4425/25 = 177.
a(2) = (2^5 + 3^5 + 4^5 + 5^5 +6^5 )/25 = (32+243+1024+3125+7776)/25 = 12200/25 = 488.
MATHEMATICA
MovingAverage[Range[40]^5, 5]/5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {177, 488, 1159, 2460, 4781, 8656}, 40] (* Harvey P. Dale, Aug 03 2024 *)
PROG
(J) (m(+/ % #) \ (1+i. 44)^(x: m))%m [m=.5 NB. See http://www.jsoftware.com
(PARI) Vec(x*(177 - 574*x + 886*x^2 - 714*x^3 + 301*x^4 - 52*x^5) / (1 - x)^6 + O(x^30)) \\ Colin Barker, Sep 18 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Robert G. Burns, Sep 12 2017
STATUS
approved