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A143689 a(n) = (3*n^2 - n + 2)/2. 8
1, 2, 6, 13, 23, 36, 52, 71, 93, 118, 146, 177, 211, 248, 288, 331, 377, 426, 478, 533, 591, 652, 716, 783, 853, 926, 1002, 1081, 1163, 1248, 1336, 1427, 1521, 1618, 1718, 1821, 1927, 2036, 2148, 2263, 2381, 2502, 2626, 2753, 2883, 3016, 3152, 3291 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals left border of triangle A033292.

Equals binomial transform of [1, 1, 3, 0, 0, 0, ...].

A242357(a(n)) = 1. - Reinhard Zumkeller, May 11 2014

LINKS

Michael De Vlieger, Table of n, a(n) for n = 0..10000

D Bevan, D Levin, P Nugent, J Pantone, L Pudwell, Pattern avoidance in forests of binary shrubs, arXiv preprint arXiv:1510:08036 [math.CO], 2015-2016.

Franck Ramaharo, Statistics on some classes of knot shadows, arXiv:1802.07701 [math.CO], 2018.

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

FORMULA

a(n) = A000326(n+1) - 3*n. (A000326 are the pentagonal numbers.)

a(n) = (3*n^2 - n + 2)/2 = A027599(n+1)/2. - R. J. Mathar, Sep 03 2008

a(n) = a(n-1) + 3*n - 2 (with a(0)=1). - Vincenzo Librandi, Nov 25 2010

a(n) = 2*a(n-1) - a(n-2) + 3.

O.g.f.: (1-x+3*x^2)/((1-x)^3). - Eric Werley, Jun 27 2011

a(n) = A104249(-n). - Bruno Berselli, Jul 08 2015

a(n) = binomial(n,2) + n^2 + 1 = A152947(n+1) + A000290(n). - Franck Maminirina Ramaharo, Mar 01 2018

MATHEMATICA

Table[(3n^2-n+2)/2, {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {1, 2, 6}, 50] (* Harvey P. Dale, May 05 2014 *)

PROG

(Haskell)

a143689 n = n*(3*n-1) `div` 2 + 1 -- Reinhard Zumkeller, May 11 2014

(PARI) a(n)=(3*n^2-n+2)/2 \\ Charles R Greathouse IV, Oct 07 2015

(Maxima) makelist(binomial(n, 2) + n^2 + 1, n, 0, 100); /* Franck Maminirina Ramaharo, Mar 01 2018 */

CROSSREFS

a(n) = A000326(n+1) - 3n. Third column of A107111.

Cf. A033292, A104249.

Sequence in context: A258603 A064960 A293503 * A180773 A011891 A184533

Adjacent sequences:  A143686 A143687 A143688 * A143690 A143691 A143692

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Aug 29 2008

EXTENSIONS

Index of A000326 in definition, formula and example corrected by R. J. Mathar, Sep 03 2008

STATUS

approved

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Last modified July 23 06:17 EDT 2018. Contains 312921 sequences. (Running on oeis4.)