OFFSET
0,2
COMMENTS
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
a(n) = ( 6n^5 + 15n^4 + 18n^3 + 12n^2 + 3n ) / 2.
G.f.: 9*x*(1+x)*(3+14*x+3*x^2)/(1-x)^6. - Colin Barker, Mar 15 2012
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). - Wesley Ivan Hurt, Apr 10 2015
EXAMPLE
Between 3^3 and 4^3 we have: 28 + 29 + ... + 62 + 63 = 1638 = a(3).
MAPLE
A048396:=n->(6*n^5+15*n^4+18*n^3+12*n^2+3*n)/2: seq(A048396(n), n=0..50); # Wesley Ivan Hurt, Apr 10 2015
MATHEMATICA
Table[Total[Range[n^3+1, (n+1)^3-1]], {n, 0, 30}] (* Harvey P. Dale, Jan 08 2011 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 27, 315, 1638, 5670, 15345}, 40] (* Harvey P. Dale, Nov 02 2024 *)
PROG
(Magma) [(6*n^5+15*n^4+18*n^3+12*n^2+3*n)/2 : n in [0..50]]; // Wesley Ivan Hurt, Apr 10 2015
(PARI) a(n)=(6*n^5+15*n^4+18*n^3+12*n^2+3*n)/2 \\ Charles R Greathouse IV, Oct 07 2015
(Python)
def A048396(n): return n*(n*(n*(n*(6*n + 15) + 18) + 12) + 3)>>1 # Chai Wah Wu, Sep 04 2024
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Patrick De Geest, Mar 15 1999
STATUS
approved