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A055999 a(n) = n*(n + 7)/2. 30
0, 4, 9, 15, 22, 30, 39, 49, 60, 72, 85, 99, 114, 130, 147, 165, 184, 204, 225, 247, 270, 294, 319, 345, 372, 400, 429, 459, 490, 522, 555, 589, 624, 660, 697, 735, 774, 814, 855, 897, 940, 984, 1029, 1075, 1122, 1170, 1219, 1269, 1320, 1372, 1425, 1479 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
If X is an n-set and Y a fixed (n-4)-subset of X then a(n-3) is equal to the number of 2-subsets of X intersecting Y. - Milan Janjic, Aug 15 2007
Numbers m >= 0 such that 8m+49 is a square. - Bruce J. Nicholson, Jul 28 2017
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, p. 193.
LINKS
Leo Tavares, Diamond illustration.
FORMULA
G.f.: x*(4-3*x)/(1-x)^3.
a(n) = A126890(n,3) for n>2. - Reinhard Zumkeller, Dec 30 2006
a(n) = A028563(n)/2. - Zerinvary Lajos, Feb 12 2007
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,4), for n>=1. - Milan Janjic, Dec 20 2008
a(n) = n + a(n-1) + 3 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010
a(n) = Sum_{k=1..n} (k+3). - Gary Detlefs, Aug 10 2010
Sum_{n>=1} 1/a(n) = 363/490. - R. J. Mathar, Jul 14 2012
a(n) = 4n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013
a(n) = Sum_{i=4..n+3} i. - Wesley Ivan Hurt, Jun 28 2013
E.g.f.: (1/2)*x*(x+8)*exp(x). - G. C. Greubel, Jul 13 2017
Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/7 - 319/1470. - Amiram Eldar, Jan 10 2021
a(n) = A000290(n+1) - A000217(n-2). - Leo Tavares, Jan 28 2023
From Amiram Eldar, Feb 12 2024: (Start)
Product_{n>=1} (1 - 1/a(n)) = 15*cos(sqrt(57)*Pi/2)/(8*Pi).
Product_{n>=1} (1 + 1/a(n)) = -63*cos(sqrt(41)*Pi/2)/(8*Pi). (End)
MATHEMATICA
Table[n*(n + 7)/2, {n, 0, 50}] (* G. C. Greubel, Jul 13 2017 *)
PROG
(PARI) a(n)=n*(n+7)/2 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Equals A000217(n+3) - 6.
Third column (m=2) of (1, 4)-Pascal triangle A095666.
Cf. A000290.
Sequence in context: A313298 A313299 A350547 * A134227 A022945 A022948
KEYWORD
easy,nonn
AUTHOR
Barry E. Williams, Jun 16 2000
EXTENSIONS
More terms from James A. Sellers, Jul 04 2000
STATUS
approved

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Last modified April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)