A021003 a(n) = (n/2)*(n^4 + 1).

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, 14314591, 16777232, 19567713

Offset: 0

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn
• easy
• changed

Comments

Magic constant for n X n X n X n hypercube (magic hypercube may not exist).

Links

• Kelvin Voskuijl, Table of n, a(n) for n = 0..10000 (terms 0..595 from Vincenzo Librandi)
• Eric Weisstein's World of Mathematics, Magic Constant.
• Eric Weisstein's World of Mathematics, Magic Tesseract.
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A000217, A006003, A027441.

Programs

Magma

[(n/2)*(n^4+1): n in [0..50]]; // Vincenzo Librandi, Apr 29 2011

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 *)

PARI

{a(n) = (n^5 + n) / 2}; /* Michael Somos, Jul 11 2017 */

Formula

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), a(0)=0, a(1)=1, a(2)=17, a(3)=123, a(4)=514, a(5)=1565. - Harvey P. Dale, Dec 18 2011

a(n) = -a(-n) for all n in Z. - Michael Somos, Jul 11 2017

From Elmo R. Oliveira, Aug 31 2025: (Start)

G.f.: x*(1 + 11*x + 36*x^2 + 11*x^3 + x^4)/(x-1)^6.

E.g.f.: x*(2 + 15*x + 25*x^2 + 10*x^3 + x^4)*exp(x)/2. (End)