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A082109 Third row of number array A082105. 8
1, 13, 33, 61, 97, 141, 193, 253, 321, 397, 481, 573, 673, 781, 897, 1021, 1153, 1293, 1441, 1597, 1761, 1933, 2113, 2301, 2497, 2701, 2913, 3133, 3361, 3597, 3841, 4093, 4353, 4621, 4897, 5181, 5473, 5773, 6081, 6397, 6721, 7053, 7393, 7741, 8097, 8461 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Define b(n)=A000217(n), the triangular numbers. Using six consecutive terms to create the vertices of a triangle at points (b(n-2),b(n-1)), (b(n),b(n+1)), and (b(n+2),b(n+3)), one fourth the area of these triangles = a(n). - J. M. Bergot, Jul 30 2013

LINKS

Table of n, a(n) for n=0..45.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1)

FORMULA

a(n) = 4n^2 + 8n + 1.

a(n) = 8*n + a(n-1) + 4 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010

G.f.: (1 + 10*x - 3*x^2)/(1-x)^3. - Bruno Berselli, Apr 18 2011

EXAMPLE

a(1)=8*1+1+4=13; a(2)=8*2+13+4=33; a(3)=8*3+33+4=61. - Vincenzo Librandi, Aug 08 2010

MATHEMATICA

s=-3; lst={}; Do[s+=n+1; AppendTo[lst, s], {n, 3, 6!, 8}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 25 2008 *)

PROG

(PARI) a(n)=4*n^2+8*n+1 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A082108.

Column 2 of array A188646.

Sequence in context: A050659 A123161 A146052 * A024839 A146177 A146194

Adjacent sequences:  A082106 A082107 A082108 * A082110 A082111 A082112

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 03 2003

STATUS

approved

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Last modified May 18 08:30 EDT 2022. Contains 353785 sequences. (Running on oeis4.)