0,3

A class of Boolean functions of n variables and rank 2.

Also, number of inscribable triangles within a (n+4)-gon sharing with them its vertices but not its sides. - Lekraj Beedassy (blekraj(AT)yahoo.com), Nov 14 2003

a(n) = A111808(n,3) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 17 2005

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

If X is an n-set and Y a fixed 2-subset of X then a(n-2) is equal to the number of (n-3)-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Jul 30 2007

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 797.

V. Jovovic, G. Kilibarda, On the number of Boolean functions in the Post classes F^{mu}_8, Diskretnaya Matematika, 11 (1999), no. 4, 127-138 (translated in Discrete Mathematics and Applications, 9, (1999), no. 6).

J. D. E. Konhauser et al., Which Way Did the Bicycle Go?, MAA 1996, p. 177.

A. McLeod and W. O. J. Moser, Counting cyclic binary strings, Math. Mag., 80 (No. 1, 2007), 29-37.

A. M. Yaglom and I. M. Yaglom: Challenging Mathematical Problems with Elementary Solutions. Vol. I. Combinatorial Analysis and Probability Theory. New York: Dover Publications, Inc., 1987, p. 13, #51 (the case k=3) (First published: San Francisco: Holden-Day, Inc., 1964)

T. D. Noe, Table of n, a(n) for n=0..1000

Milan Janjic, Two Enumerative Functions

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, December 1972 [alternative scanned copy].

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.

Eric Weisstein's World of Mathematics, Trinomial Coefficient

Index entries for sequences related to Boolean functions

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

a(n)=binomial(n+2, n-1)+binomial(n+1, n-1).

Convolution of {1, 2, 3, ...} with {2, 3, 4, ...} - Jon Perry (perry(AT)globalnet.co.uk), Jun 25 2003

a(n+2)=2*te(n)-te(n-1), e.g. a(5)=2*te(3)-te(2)=2*20-10=30, where te(n) are the tetrahedral numbers A000292 - Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003

C(3+n,3)-C(1+n,1) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 07 2006

a(n) is the coefficient of x^3 in the expansion of (1+x+x^2)^n. For example, a(1)=0 since (1+x+x^2)^1=1+x+x^2. - Peter C. Heinig (algorithms(AT)gmx.de), Apr 09 2007

E.g.f.: (x^2 +x^3/6)* exp(x). - MIchael Somos Apr 13 2007

A005581 := n->(n-1)*n*(n+4)/6;

a:=n->sum ((j+3)*j/2, j=0..n): seq(a(n), n=-1..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 17 2006

seq((n+3)*binomial(n, 3)/n, n=1..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 28 2007

A005581:=-(-2+z)/(z-1)**4; [S. Plouffe in his 1992 dissertation.]

seq(sum(binomial(n, m), m=1..3)+n^2, n=-1..44); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 19 2008

Table[(n - 1)*n*(n + 4)/6, {n, 0, 40}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 10 2006

(PARI) {a(n)= n* (n+4)* (n-1)/6} /* MIchael Somos Apr 13 2007 */

Cf. A005582. a(n)= A027907(n, 3), n >= 0 (fourth column of trinomial coefficients).

Cf. A000292.

A005586(n)= -a(-4-n).

Sequence in context: A048231 A070169 A130883 this_sequence A064468 A074470 A023550

Adjacent sequences: A005578 A005579 A005580 this_sequence A005582 A005583 A005584

nonn,easy,nice

njas

More terms from Larry Reeves (larryr(AT)acm.org), Jun 01 2000