OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = n^2*(1 + 3*n)*(3 + 5*n)/4.
G.f.: x*(8 +51*x + 30*x^2 + x^3)/(1-x)^5. - Colin Barker, Dec 17 2012
From G. C. Greubel, May 10 2019: (Start)
a(n) = Sum_{k=(n+1)..2*n} k^3.
E.g.f.: x*(32 + 150*x + 104*x^2 + 15*x^3)*exp(x)/4. (End)
EXAMPLE
a(1) = sum of 1 cube after 1^3 = 2^3 = 8,
a(2) = sum of 2 cubes after 2^3 = 3^3+4^3 = 91,
a(3) = sum of 3 cubes after 3^3 = 4^3+5^3+6^3 = 405,
a(4) = sum of 4 cubes after 4^3 = 5^3+6^3+7^3+8^3 = 1196.
MATHEMATICA
With[{cbs=Range[100]^3}, Table[Total[Take[cbs, {n+1, 2n}]], {n, 35}]] (* Harvey P. Dale, Feb 13 2011 *)
PROG
(PARI) {a(n) = n^2*(1+3*n)*(3+5*n)/4}; \\ G. C. Greubel, May 10 2019
(Magma) [n^2*(1+3*n)*(3+5*n)/4: n in [1..40]]; // G. C. Greubel, May 10 2019
(Sage) [n^2*(1+3*n)*(3+5*n)/4 for n in (1..40)] # G. C. Greubel, May 10 2019
(GAP) List([1..40], n-> n^2*(1+3*n)*(3+5*n)/4) # G. C. Greubel, May 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Zak Seidov, Apr 14 2007
STATUS
approved