OFFSET
0,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-5,2)
FORMULA
Binomial transform of [1, 1, 2, 6, 2, 6, 2, 6, ...].
From Andrew Howroyd, Sep 01 2018: (Start)
a(n) = 4*2^n - 5*n - 1 for n > 0.
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 3.
G.f.: (1 - 2*x + 2*x^2 + 4*x^3)/((1 - x)^2*(1 - 2*x)). (End)
E.g.f.: -2 - (1 + 5*x)*exp(x) + 4*exp(2*x). - G. C. Greubel, Feb 14 2021
EXAMPLE
a(3) = 16 = sum of row 3 terms of triangle A132733: (1 + 7 + 7 + 1).
a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 2, 6) = (1 + 3 + 6 + 6).
MATHEMATICA
Table[2^(n+2) -(5*n+1) -2*Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Feb 14 2021 *)
PROG
(PARI) a(n)={if(n==0, 1, 4*2^n - 5*n - 1)} \\ Andrew Howroyd, Sep 01 2018
(PARI) Vec((1 - 2*x + 2*x^2 + 4*x^3)/((1 - x)^2*(1 - 2*x)) + O(x^40)) \\ Andrew Howroyd, Sep 01 2018
(Sage) [1]+[2^(n+2) -(5*n +1) for n in (1..30)] # G. C. Greubel, Feb 14 2021
(Magma) [1] cat [2^(n+2) -(5*n +1): n in [1..30]]; // G. C. Greubel, Feb 14 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Aug 26 2007
EXTENSIONS
Terms a(10) and beyond from Andrew Howroyd, Sep 01 2018
STATUS
approved