OFFSET
0,2
COMMENTS
First bisection of A193053 (see also the numerical spiral illustrated in the Links section).
The inverse binomial transform yields 1, 9, 7, 0, 0 (0 continued).
LINKS
Bruno Berselli, Table of n, a(n) for n = 0..1000
Bruno Berselli, Illustration of initial terms.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (1 + 7*x - x^2)/(1-x)^3.
a(n) = A195020(2*n) + 2*n + 1.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = 2*a(n-1) - a(n-2) + 7.
From Elmo R. Oliveira, Dec 24 2024: (Start)
E.g.f.: exp(x)*(2 + 18*x + 7*x^2)/2.
a(n) = n + A001106(n+1). (End)
MATHEMATICA
Table[(n(7n+11))/2+1, {n, 0, 60}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 10, 26}, 60] (* Harvey P. Dale, Mar 03 2013 *)
PROG
(PARI) for(n=0, 47, print1(n*(7*n+11)/2+1", "));
(Magma) [n*(7*n+11)/2+1: n in [0..47]];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Oct 21 2011 - based on remarks and sequences by Omar E. Pol
STATUS
approved