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A062725 Write 0,1,2,3,4,... in a triangular spiral, then a(n) is the sequence found by reading the terms along the line from 0 in the direction 0,7,... 7
0, 7, 23, 48, 82, 125, 177, 238, 308, 387, 475, 572, 678, 793, 917, 1050, 1192, 1343, 1503, 1672, 1850, 2037, 2233, 2438, 2652, 2875, 3107, 3348, 3598, 3857, 4125, 4402, 4688, 4983, 5287, 5600, 5922, 6253, 6593, 6942, 7300, 7667, 8043, 8428, 8822, 9225 (list; graph; refs; listen; history; text; internal format)
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
Amelia Carolina Sparavigna, The groupoid of the Triangular Numbers and the generation of related integer sequences, Politecnico di Torino, Italy (2019).
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
Cf. A051682.
Sequence in context: A174590 A162290 A180044 * A147121 A098334 A299255
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

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)