A017282 a(n) = (10*n + 1)^2.

1, 121, 441, 961, 1681, 2601, 3721, 5041, 6561, 8281, 10201, 12321, 14641, 17161, 19881, 22801, 25921, 29241, 32761, 36481, 40401, 44521, 48841, 53361, 58081, 63001, 68121, 73441, 78961, 84681, 90601, 96721, 103041, 109561, 116281, 123201

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), A017174 (m=9), this sequence (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

Cf. A017281.

Programs

Magma

[(10*n+1)^2: n in [0..35]]; // Vincenzo Librandi, Jul 30 2011

Mathematica

(* Programs from Michael De Vlieger, Mar 30 2017 *)
Table[(10 n+1)^2, {n, 0, 35}]
FoldList[#1 + 200 #2 - 80 &, 1, Range@ 35]
CoefficientList[Series[(1+118x+81x^2)/(1-x)^3, {x,0,35}], x] (* End *)
LinearRecurrence[{3,-3,1},{1,121,441},40] (* Harvey P. Dale, Sep 21 2017 *)

PARI

for(n=0, 35, print1((10*n+1)^2", ")); \\ Bruno Berselli, Jul 30 2011

SageMath

[(10*n+1)^2 for n in range(51)] # G. C. Greubel, Dec 24 2022

Formula

G.f.: (1+118*x+81*x^2)/(1-x)^3. - Bruno Berselli, Jul 30 2011

a(n) = a(n-1) + 40*(5*n-2), n > 0; a(0)=1. - Miquel Cerda, Oct 30 2016

a(n) = A017281(n)^2. - Michel Marcus, Oct 30 2016

E.g.f.: (1 +120*x +100*x^2)*exp(x). - G. C. Greubel, Dec 24 2022

Extensions

More terms from Bruno Berselli, Jul 30 2011