OFFSET
0,2
COMMENTS
Conjecture: A255437(a(n)) = 2*n+1, i.e. a(n) = gives the position of the first occurrence of 2*n+1 in A255437. - Reinhard Zumkeller, Mar 23 2015
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (1+2*n+2*n^2) * (1+3*n+3*n^2).
G.f.: (1+30*x+82*x^2+30*x^3+x^4)/(1-x)^5. - Colin Barker, Jul 30 2012
E.g.f.: exp(x)*(1 + 34*x + 89*x^2 + 48*x^3 + 6*x^4). - Stefano Spezia, Mar 10 2024
EXAMPLE
Sample flows (. represents a space):
Numbers in long rows are on cell walls showing velocity rightward.
Numbers in long columns are on cell floors showing velocity downwards.
3 X 3 cell centers are at the intersection of long rows and long columns.
n=1:
.. 0 . 0 . 0
.0. -1. -1 . 0
.. 1 . 0. -1
.0 . 0 . 0 . 0
.. 1 . 0. -1
.0 . 1 . 1 . 0
.. 0 . 0 . 0
n=2:
.. 0 . 0 . 0
.0. -2. -1 . 0
.. 2. -1. -1
.0 . 0. -1 . 0
.. 2 . 0. -2
.0 . 2 . 2 . 0
.. 0 . 0 . 0
PROG
(Haskell)
a068722 n = (1 + 2 * n + 2 * n ^ 2) * (1 + 3 * n + 3 * n ^ 2)
-- Reinhard Zumkeller, Mar 23 2015
(PARI) a(n)=(1+2*n+2*n^2)*(1+3*n+3*n^2) \\ Charles R Greathouse IV, Apr 08 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Feb 26 2002
EXTENSIONS
Formula corrected by Colin Barker, Jul 30 2012
STATUS
approved