A016161 Expansion of g.f. 1/((1-5*x)*(1-7*x)).

1, 12, 109, 888, 6841, 51012, 372709, 2687088, 19200241, 136354812, 964249309, 6798573288, 47834153641, 336059778612, 2358521965909, 16540171339488, 115933787267041, 812299450322412, 5689910849522509

Offset

0,2

Comments

Also, this is the number of incongruent integer-edged Heron triangles whose circumdiameter is the product of n distinct primes each of shape 4k + 1. Cf. A003462, A109021. - R. K. Guy, Jan 31 2007

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (12,-35).

Formula

From R. J. Mathar, Sep 18 2008: (Start)

a(n) = (7^(n+1) - 5^(n+1))/2 = A081200(n+1).

Binomial transform of A080962. (End)

a(n) = 7*a(n-1) + 5^n. - Vincenzo Librandi, Feb 09 2011

E.g.f.: exp(5*x)*(7*exp(2*x) - 5)/2. - Stefano Spezia, Oct 25 2023

Mathematica

CoefficientList[Series[1/((1-5x)(1-7x)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {12, -35}, {1, 12}, 30] (* Harvey P. Dale, Nov 16 2021 *)

Prog

(PARI) Vec(1/((1-5*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
(Magma) [n le 2 select 12^(n-1) else 12*Self(n-1) -35*Self(n-2): n in [1..30]]; // G. C. Greubel, Nov 09 2024
(SageMath)
A016161=BinaryRecurrenceSequence(12, -35, 1, 12)
[A016161(n) for n in range(31)] # G. C. Greubel, Nov 09 2024

Crossrefs

Cf. A003462, A080962, A081200, A109021.

Cf. A016162, A016163, A016164, A016165, A016166.

Sequence in context: A011999 A128877 A085797 * A081200 A351161 A016214

Adjacent sequences: A016158 A016159 A016160 * A016162 A016163 A016164

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved