A180270 Integers of the form (k^12 - k^8 - k^4 + 1)/512.

0, 1025, 476073, 27022500, 551536100, 6129324225, 45502479225, 253405810448, 1137920432400, 4322847530025, 14366776735025, 42801847892100, 116415023802948, 293153032943225, 691043521403025, 1538402208782400

Offset: 1

Author

Michel Lagneau, Aug 23 2010

Keywords

• nonn
• easy

Examples

			a(2) = 1025 is in the sequence because (3^12 - 3^8 - 3^4 + 1)/512 = 524800/512 = 1025.
		

Links

• B. Berselli, Table of n, a(n) for n = 1..100000. [From _Bruno Berselli_, Sep 21 2010]

Programs

Maple

for n from 1 by 2 to 60 do: x:= (n^12-n^8 -n^4+1)/512: printf(`%d, `, x):od: # incomplete program which also prints rationals, R. J. Mathar

Mathematica

Select[Table[(k^12-k^8-k^4+1)/512,{k,40}],IntegerQ]  (* Harvey P. Dale, Jan 23 2011 *)

Formula

Integers of the form (k^4+1)*( (k-1)*(k+1)*(k^2+1) )^2/512.

a(n) = ((2*n-1)^4+1)*((n-1)*n*(n^2+(n-1)^2))^2/8 (for k=2n-1).

a(n) = A175110(n-1)*(A001844(n-1)*A000217(n-1))^2. - Bruno Berselli, Sep 21 2010

Extensions

Comment converted to formula by R. J. Mathar, Aug 25 2010

Example corrected and general term of the sequence rewritten by Bruno Berselli, Sep 22 2010