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A046691 a(n) = (n^2 + 5*n - 2)/2. 16
-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
a(n-1) yields the second Betti number of a path graph on n vertices. - Samuel J. Bevins, Nov 27 2022
LINKS
P. Di Francesco, O. Golinelli and E. Guitter, Meander, folding and arch statistics, arXiv:hep-th/9506030, 1995.
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
a(n) + a(n+1) = A028884(n). - R. J. Mathar, Mar 13 2021
a(n) = A000217(n+2) - 4. - G. C. Greubel, Jul 31 2022
Sum_{n>=0} 1/a(n) = 7/12 + 2*Pi*tan(sqrt(33)*Pi/2)/sqrt(33). - Vaclav Kotesovec, Dec 31 2022
MAPLE
seq(binomial(n+3, 2)-4, n=0..49); # Zerinvary Lajos, Jan 13 2007
MATHEMATICA
Table[(n^2 +5n -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
(Magma) [Binomial(n+3, 2) -4: n in [0..50]]; // G. C. Greubel, Jul 31 2022
(SageMath) [(n^2 +5*n -2)/2 for n in (0..50)] # G. C. Greubel, Jul 31 2022
CROSSREFS
Triangular numbers (A000217) minus 4. Cf. A027379.
Sequence in context: A212459 A099056 A347315 * A098167 A081689 A231559
KEYWORD
sign,easy
AUTHOR
STATUS
approved

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Last modified March 5 08:03 EST 2024. Contains 370538 sequences. (Running on oeis4.)