OFFSET
0,3
COMMENTS
Starting with offset 1 = binomial transform of (1, 8, 25, 30, 12, 0, 0, 0, ...). - Gary W. Adamson, May 20 2009
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..680
Eric Weisstein's World of Mathematics, Magic Constant
Eric Weisstein's World of Mathematics, Magic Cube
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
O.g.f.: x*(1+4*x+7*x^2)/(1-x)^5. - R. J. Mathar, Feb 13 2008
a(n) = Sum_{k=n..n^2} k; for n>0: a(n) = A037270(n) - A000217(n-1). - Reinhard Zumkeller, Jul 06 2010
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Wesley Ivan Hurt, Aug 13 2014
a(n) = ( Sum_{i=1..n^3} i ) / n^2, for n > 0. - Wesley Ivan Hurt, Aug 13 2014
a(n) = (n+1)*(a(n-1)/(n-1) + n*(n-1)), a(0)=0, a(1)=1. - Vladimir Kruchinin, Oct 10 2018
MAPLE
MATHEMATICA
Table[(n^4 + n)/2, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 13 2014 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 9, 42, 130}, 40] (* Harvey P. Dale, Apr 09 2018 *)
PROG
(Magma) [(n^4+n)/2: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
(PARI) a(n)=(n^4 + n)/2 \\ Charles R Greathouse IV, Jul 28 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Wesley Ivan Hurt, Aug 13 2014
STATUS
approved