A060189 A column and diagonal of A060187 (k=3).

1, 23, 230, 1682, 10543, 60657, 331612, 1756340, 9116141, 46702427, 237231970, 1198382694, 6031771195, 30287995733, 151856096504, 760614930344, 3807336276505, 19050241098975, 95294209168414, 476607030432890

Offset: 3

Author

N. J. A. Sloane, Mar 20 2001

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 3..1000
• P. A. MacMahon, The divisors of numbers, Proc. London Math. Soc., (2) 19 (1920), 305-340; Coll. Papers II, pp. 267-302.
• Index entries for linear recurrences with constant coefficients, signature (14,-75,196,-263,174,-45).

Crossrefs

Cf. A060187.

Programs

Magma

[5^(n-1) -n*3^(n-1) +n*(n-1)/2: n in [3..40]]; // G. C. Greubel, Jul 31 2024

Mathematica

Table[5^(n-1) -n*3^(n-1) +n*(n-1)/2, {n,3,40}] (* G. C. Greubel, Jul 31 2024 *)

SageMath

[5^(n-1) -n*3^(n-1) +n*(n-1)//2 for n in range(3,41)] # G. C. Greubel, Jul 31 2024

Formula

a(n) = 5^(n-1) - n*3^(n-1) + n*(n-1)/2. - Ralf Stephan, May 08 2004

G.f.: x^3*(1 + 9*x - 17*x^2 - 9*x^3) / ((1-x)^3*(1-3*x)^2*(1-5*x)). - Colin Barker, Dec 19 2012

From Wolfdieter Lang, Apr 17 2017: (Start)

a(n) = A060187(n, 3) , n >= 3 (and 0 for n = 0,1,2).

a(n) = A060187(n, n-2), n >= 3 (and 0 for n = 0,1,2).

E.g.f.: (2*exp(5*x) - 10*x*exp(3*x) + 5*x^2*exp(x) - 2)/10. (End)

Extensions

More terms from Vladeta Jovovic, Mar 20 2001