0,2

Binomial transform of (1,4,6,4,0,0,0,.......) - Paul Barry (pbarry(AT)wit.ie), Jul 01 2003

If X is an n-set and Y a fixed 4-subset of X then a(n-4) is equal to the number of 4-subsets of X intersecting Y. - Milan R. Janjic (agnus(AT)blic.net), Jul 30 2007

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.

T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (10).

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558.

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

Milan Janjic, Two Enumerative Functions

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.

a(n)=(1/3)*(2*n+1)*(n^2+n+3). G.f.: (1-x^4)/(1-x)^5.

a(n)=C(n, 0)+4C(n, 1)+6C(n, 2)+4C(n, 3) - Paul Barry (pbarry(AT)wit.ie), Jul 01 2003

a(n) is the sum of 4 consecutive tetrahedral (or pyramidal) numbers: C(n+3,3) = (n+1)(n+2)(n+3)/6 = A000292(n). a(n) = A000292(n-3) + A000292(n-2) + A000292(n-1) + A000292(n). - Alexander Adamchuk (alex(AT)kolmogorov.com), May 20 2006

binomial(n+6,n+3)+binomial(n+5,n+2)+binomial(n+4,n+1)+binomial(n+3,n).

A005894:=(z+1)*(1+z**2)/(z-1)**4; [Conjectured by S. Plouffe in his 1992 dissertation.]

(1/12)*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.

Cf. A000292.

Sequence in context: A061829 A063382 A069983 this_sequence A015622 A000750 A008487

Adjacent sequences: A005891 A005892 A005893 this_sequence A005895 A005896 A005897

nonn,easy,nice

njas