OFFSET
0,2
COMMENTS
Inverse binomial transform of this sequence is A090129.
Conjecture: Last digit of a(n) has repeating pattern of 20 digits as follows: {1, 3, 7, 7, 5, 7, 1, 1, 9, 1, 5, 5, 3, 5, 9, 9, 7, 9, 3, 3}, with an equal frequency of the five odd digits.
LINKS
FORMULA
a(n) = 3*a(n-1) - 2*(n-1), with a(0) = 1.
(a(n+1) - a(n))/2 = A007051(n).
From Colin Barker, Dec 17 2013: (Start)
a(n) = (1 + 3^n + 2*n)/2.
a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).
G.f.: (x^2+2*x-1) / ((x-1)^2*(3*x-1)). (End)
E.g.f.: exp(x)*(1 + exp(2*x) + 2*x)/2. - Stefano Spezia, Mar 20 2022
EXAMPLE
a(1) = 3*1 - 2*0 = 3;
a(2) = 3*3 - 2*1 = 7.
MATHEMATICA
LinearRecurrence[{5, -7, 3}, {1, 3, 7}, 30] (* Harvey P. Dale, Feb 13 2015 *)
PROG
(PARI) Vec((x^2+2*x-1)/((x-1)^2*(3*x-1)) + O(x^100)) \\ Colin Barker, Dec 17 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Richard R. Forberg, Dec 14 2013
STATUS
approved