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A000297 a(n) = (n+1)*(n+3)*(n+8)/6.
(Formerly M3434 N1393)
8
0, 4, 12, 25, 44, 70, 104, 147, 200, 264, 340, 429, 532, 650, 784, 935, 1104, 1292, 1500, 1729, 1980, 2254, 2552, 2875, 3224, 3600, 4004, 4437, 4900, 5394, 5920, 6479, 7072, 7700, 8364, 9065, 9804, 10582, 11400, 12259, 13160, 14104, 15092, 16125, 17204 (list; graph; refs; listen; history; text; internal format)
OFFSET

-1,2

COMMENTS

If Y and Z are 2-blocks of an n-set X then, for n>=4, a(n-5) is the number of (n-3)-subsets of X intersecting both Y and Z. - Milan Janjic, Nov 09 2007

REFERENCES

J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 150.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = -1..1000

P. Erdős, R. K. Guy and J. W. Moon, On refining partitions, J. London Math. Soc., 9 (1975), 565-570.

Milan Janjic, Two Enumerative Functions

M. Janjic and B. Petkovic, A Counting Function, arXiv preprint arXiv:1301.4550, 2013. - From N. J. A. Sloane, Feb 13 2013

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

A. Scott, T. Delaney and V. E. Hoggatt, Jr., The tribonacci sequence, Fib. Quart., 15 (1977), 193-200.

FORMULA

G.f.: (2-x)^2 / (1-x)^4.

a(n) = Sum_{k=3..n} n*(k+1)/3, n>=2. - Zerinvary Lajos, Jan 29 2008

G.f.: 2*x*W(0), where W(k) = 1 + 1/( 1 - x*(k+2)*(k+4)*(k+9)/(x*(k+2)*(k+4)*(k+9) + (k+1)*(k+3)*(k+8)/W(k+1) )) ); (continued fraction). - Sergei N. Gladkovskii, Aug 24 2013

With offset 3, for n>3, a(n) = 4 binomial(n-2,2) + binomial(n-3,3), comprising the fourth column of A267633. - Tom Copeland, Jan 25 2016

From Bob Selcoe, Apr 02 2016 (Start):

a(n) = A000292(n+3) - 2n - 6.

a(n) = a(n-1) + (n^2 + 7n + 8)/2.

(End)

MAPLE

A000297:=(z-2)**2/(z-1)**4; # Simon Plouffe in his 1992 dissertation

for n from 2 to 46 do printf(`%d, `, sum(n*(k+1)/3, k=3..n)) od: # Zerinvary Lajos, Jan 29 2008

MATHEMATICA

Table[(n + 1)*(n + 3)*(n + 8)/6, {n, -1, 100}]

PROG

(PARI) a(n) = (n+1)*(n+3)*(n+8)/6; \\ Altug Alkan, Jan 10 2015

CROSSREFS

Cf. A000292.

Sequence in context: A225254 A008186 A008264 * A078618 A062883 A008176

Adjacent sequences:  A000294 A000295 A000296 * A000298 A000299 A000300

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from James A. Sellers, Sep 08 2000

STATUS

approved

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Last modified March 27 02:08 EDT 2017. Contains 284143 sequences.