A016994 a(n) = (7*n + 1)^2.

1, 64, 225, 484, 841, 1296, 1849, 2500, 3249, 4096, 5041, 6084, 7225, 8464, 9801, 11236, 12769, 14400, 16129, 17956, 19881, 21904, 24025, 26244, 28561, 30976, 33489, 36100, 38809, 41616, 44521, 47524

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m-3), A016814 (m=4), A016862 (m=5), A016922 (m=6), this sequence (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

Programs

Magma

[(7*n+1)^2: n in [0..40]]; // Vincenzo Librandi, Jul 13 2011

Mathematica

(7Range[0,50]+1)^2  (* Harvey P. Dale, Mar 05 2011 *)
CoefficientList[Series[(1+61*x+36*x^2)/(1-x)^3, {x,0,40}], x] (* Vincenzo Librandi, Jan 27 2013 *)

PARI

a(n)=(7*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[(7*n+1)^2 for n in range(41)] # G. C. Greubel, Dec 28 2022

Formula

G.f.: (1 + 61*x + 36*x^2)/(1-x)^3. - Vincenzo Librandi, Jan 27 2013

From G. C. Greubel, Dec 28 2022: (Start)

a(2*n) = A134934(n).

a(2*n+1) = 4*A017030(n).

E.g.f.: (1 + 63*x + 49*x^2)*exp(x). (End)

Sum_{n>=0} 1/a(n) = Psi'(1/7)/49 = 1.027703498712483534.. - R. J. Mathar, May 07 2024