login
A021003
a(n) = (n/2)*(n^4+1).
5
0, 1, 17, 123, 514, 1565, 3891, 8407, 16388, 29529, 50005, 80531, 124422, 185653, 268919, 379695, 524296, 709937, 944793, 1238059, 1600010, 2042061, 2576827, 3218183, 3981324, 4882825, 5940701, 7174467, 8605198, 10255589, 12150015
OFFSET
0,3
COMMENTS
Magic constant for n X n X n X n hypercube (magic hypercube may not exist).
LINKS
Eric Weisstein's World of Mathematics, Magic Constant.
Eric Weisstein's World of Mathematics, Magic Tesseract
FORMULA
a(0)=0, a(1)=1, a(2)=17, a(3)=123, a(4)=514, a(5)=1565, 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). - Harvey P. Dale, Dec 18 2011
a(n) = -a(-n) for all n in Z. - Michael Somos, Jul 11 2017
MATHEMATICA
Table[(n(n^4+1))/2, {n, 0, 40}] (* or *) LinearRecurrence[ {6, -15, 20, -15, 6, -1}, {0, 1, 17, 123, 514, 1565}, 40] (* Harvey P. Dale, Dec 18 2011 *)
PROG
(Magma) [(n/2)*(n^4+1): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
(PARI) {a(n) = (n^5 + n) / 2}; /* Michael Somos, Jul 11 2017 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arlin Anderson (starship1(AT)gmail.com)
STATUS
approved