A016832 a(n) = (4*n + 2)^8.

256, 1679616, 100000000, 1475789056, 11019960576, 54875873536, 208827064576, 656100000000, 1785793904896, 4347792138496, 9682651996416, 20047612231936, 39062500000000, 72301961339136, 128063081718016, 218340105584896, 360040606269696, 576480100000000, 899194740203776

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Formula

From Harvey P. Dale, May 20 2011: (Start)

a(0)=256, a(1)=1679616, a(2)=100000000, a(3)=1475789056, a(4)=11019960576, a(5)=54875873536, a(6)=208827064576, a(7)=656100000000, a(8)=1785793904896, a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9).

G.f.: -((256*(1 + 6552*x + 331612*x^2 + 2485288*x^3 + 4675014*x^4 + 2485288*x^5 + 331612*x^6 + 6552*x^7 + x^8))/(-1+x)^9). (End)

From Amiram Eldar, Apr 21 2023: (Start)

a(n) = A016825(n)^8.

a(n) = 2^8*A016760(n).

Sum_{n>=0} 1/a(n) = 17*Pi^8/41287680. (End)

Mathematica

(4Range[0, 20]+2)^8 (* Harvey P. Dale, May 20 2011 *)

Prog

(Magma) [(4*n+2)^8: n in [0..30] ]; // Vincenzo Librandi, May 23 2011

Crossrefs

Cf. A016760, A016825.

Sequence in context: A278142 A013759 A283933 * A103350 A069447 A227606

Adjacent sequences: A016829 A016830 A016831 * A016833 A016834 A016835

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved