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A046691 a(n) = (n^2+5*n-2)/2. 11
-1, 2, 6, 11, 17, 24, 32, 41, 51, 62, 74, 87, 101, 116, 132, 149, 167, 186, 206, 227, 249, 272, 296, 321, 347, 374, 402, 431, 461, 492, 524, 557, 591, 626, 662, 699, 737, 776, 816, 857, 899, 942, 986, 1031, 1077, 1124, 1172, 1221, 1271, 1322 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If Y_i (i=1,2,3,4) are 2-blocks of an n-set X then, for n>=8, a(n-3) is the number of (n-2)-subsets of X intersecting each Y_i (i=1,2,3,4). - Milan Janjic, Nov 09 2007

Numbers m > -3 such that 8*m + 33 is a square. - Bruno Berselli, Aug 20 2015

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

Milan Janjic, Two Enumerative Functions

P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics, arXiv:hep-th/9506030, 1995.

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

FORMULA

G.f.: (-1 + 5*x - 3*x^2)/(1 - x)^3.

a(n) = a(n-1) + n + 2 with a(0) = -1. - Vincenzo Librandi, Nov 18 2010

a(n) = 3*A000096(n-1) - 2*A000096(n-2), with A000096(-2)=A000096(-1)=-1. - Bruno Berselli, Dec 17 2014

a(n) = 2*A000217(n) - A000217(n-2), with A000217(-2)=1, A000217(-1)=0. - Bruno Berselli, Oct 13 2016

E.g.f.: (1/2)*(x^2 + 6*x - 2)*exp(x). - G. C. Greubel, Jul 13 2017

MAPLE

seq(binomial(n, 2)-4, n=3..52); # Zerinvary Lajos, Jan 13 2007

with (combinat):seq((fibonacci(3, n)+n-9)/2, n=2..51); # Zerinvary Lajos, Jun 07 2008

MATHEMATICA

i=3; s=-1; lst={}; Do[s+=n+i; If[s>=0, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 29 2008 *)

s=-1; lst={}; Do[s+=n-2; If[s>-2, AppendTo[lst, s]], {n, 0, 6!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 04 2008 *)

Table[(n^2 + 5 n - 2)/2, {n, 0, 50}] (* Bruno Berselli, Dec 17 2014 *)

PROG

(PARI) a(n)=(n^2+5*n-2)/2 \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Triangular numbers (A000217) minus 4. Cf. A027379.

Cf. A000096, A002522.

Sequence in context: A217687 A212459 A099056 * A098167 A081689 A176708

Adjacent sequences:  A046688 A046689 A046690 * A046692 A046693 A046694

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 24 01:11 EST 2020. Contains 332195 sequences. (Running on oeis4.)