OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From G. C. Greubel, Oct 12 2019: (Start)
G.f.: (1 + 27*x + 8*x^2)/(1-x)^3.
E.g.f.: (1 + 29*x + 18*x^2)*exp(x). (End)
Sum 1/a(n) = -Psi(1/9)/7 -gamma/7 -2*log(2)/7 = 1.0634904644443440.. where gamma = A001620, Psi(1/9) = -A354636.
From Elmo R. Oliveira, Dec 17 2025: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
MAPLE
seq((2*n+1)*(9*n+1), n=0..50); # G. C. Greubel, Oct 12 2019
MATHEMATICA
Table[(2*n+1)*(9*n+1), {n, 0, 50}] (* G. C. Greubel, Oct 12 2019 *)
PROG
(PARI) a(n)=(2*n+1)*(9*n+1) \\ Charles R Greathouse IV, Jun 17 2017
(Magma) [(2*n+1)*(9*n+1): n in [0..50]]; // G. C. Greubel, Oct 12 2019
(SageMath) [(2*n+1)*(9*n+1) for n in range(50)] # G. C. Greubel, Oct 12 2019
(GAP) List([0..50], n-> (2*n+1)*(9*n+1)); # G. C. Greubel, Oct 12 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
