A085036 a(n) = (5*n+2)*(5*n+7).

14, 84, 204, 374, 594, 864, 1184, 1554, 1974, 2444, 2964, 3534, 4154, 4824, 5544, 6314, 7134, 8004, 8924, 9894, 10914, 11984, 13104, 14274, 15494, 16764, 18084, 19454, 20874, 22344, 23864, 25434, 27054, 28724, 30444, 32214, 34034, 35904, 37824, 39794, 41814

Offset

0,1

Comments

1 = 2/7 + Sum(n=1,inf.,25/a(n)) = 2/7 + 25/84 + 25/204 + 25/374 + 25/594...+...; with partial sums: 2/7, 7/12, 12/17, 17/22...(5n+2)/(5n+7)...==>1

Links

Table of n, a(n) for n=0..40.

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

Formula

a(n) = 25*n^2 + 45*n + 14.

From Elmo R. Oliveira, Nov 11 2025: (Start)

G.f.: 2*(7 + 21*x - 3*x^2)/(1-x)^3.

E.g.f.: (14 + 70*x + 25*x^2)*exp(x).

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

Mathematica

Table[(5n+2)(5n+7), {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {14, 84, 204}, 60] (* Harvey P. Dale, Jun 17 2023 *)

Prog

(PARI) a(n)=(5*n+2)*(5*n+7) \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A376290 A323415 A166389 * A107935 A008451 A033276

Adjacent sequences: A085033 A085034 A085035 * A085037 A085038 A085039

Keyword

nonn,easy

Author

Gary W. Adamson, Jun 19 2003

Extensions

Corrected by Douglas McNeil and Charles R Greathouse IV, Aug 31 2010

Status

approved