

A139271


a(n) = 2*n*(4*n3).


16



0, 2, 20, 54, 104, 170, 252, 350, 464, 594, 740, 902, 1080, 1274, 1484, 1710, 1952, 2210, 2484, 2774, 3080, 3402, 3740, 4094, 4464, 4850, 5252, 5670, 6104, 6554, 7020, 7502, 8000, 8514, 9044, 9590, 10152, 10730, 11324, 11934, 12560
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OFFSET

0,2


COMMENTS

Sequence found by reading the line from 0, in the direction 0, 2, ..., in the square spiral whose vertices are the triangular numbers A000217. Opposite numbers to the members of A033585 in the same spiral.
Twice decagonal numbers (or twice 10gonal numbers).  Omar E. Pol, May 15 2008


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = 8*n^2  6*n.
Sequences of the form a(n) = 8*n^2 + c*n have generating functions x{c+8+(8c)x} / (1x)^3 and recurrence a(n) = 3a(n1)  3a(n2) + a(n3). The inverse binomial transform is 0, c+8, 16, 0, 0, ... (0 continued). This applies to A139271A139278, positive or negative c.  R. J. Mathar, May 12 2008
a(n) = A001107(n)*2.  Omar E. Pol, May 15 2008
a(n) = 16*n + a(n1)  14 (with a(0)=0).  Vincenzo Librandi, Aug 03 2010
From G. C. Greubel, Jul 18 2017: (start)
G.f.: (2*x)*(7*x+1)/(1x)^3.
E.g.f.: (8*x^2 + 2*x)*exp(x). (End)


MATHEMATICA

s=0; lst={s}; Do[s+=n; AppendTo[lst, s], {n, 2, 6!, 16}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 02 2009 *)
Table[8n^26n, {n, 0, 40}] (* or *) LinearRecurrence[{3, 3, 1}, {0, 2, 20}, 50] (* Harvey P. Dale, Sep 26 2016 *)


PROG

(PARI) a(n)=2*n*(4*n3) \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A000217, A014634, A014635, A033585, A033586, A033587, A035008, A051870, A069129, A085250, A139272, A139273, A139274, A139275, A139276, A139278, A139279, A139280, A139281, A139282.
Cf. A001107.
Cf. numbers of the form n*(n*kk+4))/2 listed in A226488 (this sequence is the case k=16).  Bruno Berselli, Jun 10 2013
Sequence in context: A261838 A225065 A059211 * A133217 A001504 A192351
Adjacent sequences: A139268 A139269 A139270 * A139272 A139273 A139274


KEYWORD

easy,nonn


AUTHOR

Omar E. Pol, Apr 26 2008


EXTENSIONS

Corrected by Harvey P. Dale, Sep 26 2016


STATUS

approved



