OFFSET
0,2
COMMENTS
Central terms of triangle A245300. - Reinhard Zumkeller, Jul 17 2014
Digital root of a(n) = A180597(n). - Gionata Neri, Apr 29 2015
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Amelia Carolina Sparavigna, The groupoid of the Triangular Numbers and the generation of related integer sequences, Politecnico di Torino, Italy (2019).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n*(9*n+5)/2.
a(n) = 9*n + a(n-1) - 2 with a(0)=0. - Vincenzo Librandi, Aug 07 2010
From Colin Barker, Jul 07 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(7+2*x)/(1-x)^3. (End)
a(n) = A218470(9*n+6). - Philippe Deléham, Mar 27 2013
a(n) = a(n-1) + A017245(n-1), a(0)=0. - Gionata Neri, Apr 30 2015
EXAMPLE
The spiral begins:
.
15
/ \
16 14
/ \
17 3 13
/ / \ \
18 4 2 12
/ / \ \
19 5 0---1 11
/ / \
20 6---7---8---9--10
.
MATHEMATICA
s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 7!, 9}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)
CoefficientList[Series[x (7 + 2 x)/(1 - x)^3, {x, 0, 45}], x] (* Michael De Vlieger, Jan 11 2020 *)
PROG
(Haskell)
a062725 n = n * (9 * n + 5) `div` 2 -- Reinhard Zumkeller, Jul 17 2014
(PARI) a(n) = n*(9*n+5)/2 \\ Charles R Greathouse IV, Apr 30 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Floor van Lamoen, Jul 21 2001
EXTENSIONS
Formula that confused indices corrected by R. J. Mathar, Jun 04 2010
STATUS
approved