A134934 a(n) = (14*n+1)^2.

1, 225, 841, 1849, 3249, 5041, 7225, 9801, 12769, 16129, 19881, 24025, 28561, 33489, 38809, 44521, 50625, 57121, 64009, 71289, 78961, 87025, 95481, 104329, 113569, 123201, 133225, 143641, 154449, 165649, 177241, 189225, 201601, 214369, 227529, 241081

Offset: 0

Author

Hans Isdahl, Jan 26 2008

Keywords

• nonn
• easy

Comments

Number of rats in population after n years, starting with one rat at year 0 (see A016754 for more details).

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), A017282 (m=10), A017402 (m=11), A017534 (m=12), this sequence (m=14).

Cf. A016754.

Programs

Magma

[(14*n+1)^2: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011

Mathematica

(14*Range[0,50]+1)^2 (* G. C. Greubel, Dec 24 2022 *)

PARI

a(n)=(14*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

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

Formula

O.g.f.: (1+222*x+169*x^2)/(1-x)^3 = 169/(1-x) - 560/(1-x)^2 + 392/(1-x)^3. - R. J. Mathar, Jan 31 2008

a(n) = A016754(7*n).

E.g.f.: (1 + 224*x + 196*x^2)*exp(x). - G. C. Greubel, Dec 24 2022