A017174 a(n) = (9*n + 1)^2.

1, 100, 361, 784, 1369, 2116, 3025, 4096, 5329, 6724, 8281, 10000, 11881, 13924, 16129, 18496, 21025, 23716, 26569, 29584, 32761, 36100, 39601, 43264, 47089, 51076, 55225, 59536, 64009, 68644

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), A016994 (m=7), A017078 (m=8), this sequence (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

Cf. A017222.

Programs

Magma

[(9*n+1)^2: n in [0..40]]; // Vincenzo Librandi, Aug 25 2011

Mathematica

(9*Range[0,40] +1)^2 (* G. C. Greubel, Dec 28 2022 *)
LinearRecurrence[{3,-3,1},{1,100,361},50] (* Harvey P. Dale, Feb 25 2024 *)

PARI

a(n)=(9*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

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

Formula

G.f.: x*(1 + 97*x + 64*x^2)/(1-x)^3. - Bruno Berselli, Aug 25 2011

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

a(2*n) = A016754(9*n).

a(2*n+1) = 4*A017222(n).

E.g.f.: (1 + 99*x + 81*x^2)*exp(x). (End)