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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 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

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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(9n+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

a(1)=9*1+0-2=7; a(2)=9*2+7-2=23; a(3)=9*3+23-2=48. - Vincenzo Librandi, Aug 07 2010

MATHEMATICA

s=0; lst={s}; Do[s+=n++ +7; AppendTo[lst, s], {n, 0, 7!, 9}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *)

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

Adjacent sequences:  A062722 A062723 A062724 * A062726 A062727 A062728

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 July 22 17:31 EDT 2018. Contains 312914 sequences. (Running on oeis4.)