A016982 a(n) = (7*n)^2.

0, 49, 196, 441, 784, 1225, 1764, 2401, 3136, 3969, 4900, 5929, 7056, 8281, 9604, 11025, 12544, 14161, 15876, 17689, 19600, 21609, 23716, 25921, 28224, 30625, 33124, 35721, 38416, 41209, 44100, 47089, 50176, 53361, 56644, 60025, 63504, 67081, 70756, 74529, 78400

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Amiram Eldar, Jan 25 2021: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/294.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/588.

Product_{n>=1} (1 + 1/a(n)) = sinh(Pi/7)/(Pi/7).

Product_{n>=1} (1 - 1/a(n)) = sin(Pi/7)/(Pi/7). (End)

From Elmo R. Oliveira, Nov 29 2024: (Start)

G.f.: 49*x*(1 + x)/(1-x)^3.

E.g.f.: 49*x*(1 + x)*exp(x).

a(n) = 49*A000290(n) = A008589(n)^2 = A000290(A008589(n)).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

Prog

(Magma) [(7*n)^2: n in [0..50]]; // Vincenzo Librandi, May 21 2011
(PARI) a(n)=(7*n)^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A000290, A008589.

Sequence in context: A158638 A198386 A351663 * A157919 A297895 A204709

Adjacent sequences: A016979 A016980 A016981 * A016983 A016984 A016985

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved