A006004 a(n) = C(n+2,3) + C(n,3) + C(n-1,3). (Formerly M3412)

1, 4, 11, 25, 49, 86, 139, 211, 305, 424, 571, 749, 961, 1210, 1499, 1831, 2209, 2636, 3115, 3649, 4241, 4894, 5611, 6395, 7249, 8176, 9179, 10261, 11425, 12674, 14011, 15439, 16961, 18580, 20299, 22121, 24049, 26086, 28235, 30499, 32881, 35384, 38011, 40765

Offset

1,2

Comments

Equals binomial transform of [1, 3, 4, 3, 0, 0, 0, ...]. Example: a(4) = 25 = (1, 3, 3, 1) dot (1, 3, 4, 3) = (1 + 9 + 12 + 3). - Gary W. Adamson, Jul 25 2008

References

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926.

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

S. M. Losanitsch, Die Isomerie-Arten bei den Homologen der Paraffin-Reihe, Chem. Ber. 30 (1897), 1917-1926. (Annotated scanned copy)

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Formula

a(n) = (n^3 - 2n^2 + 5n - 2)/2.

G.f.: (x^3+x^2+1)/(x-1)^4. - Harvey P. Dale, Jun 15 2011

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), with a(0)=1, a(1)=4, a(2)=11, a(3)=25. - Harvey P. Dale, Jun 15 2011

Maple

A006004:=n->(n^3 - 2*n^2 + 5*n - 2)/2; seq(A006004(n), n=1..50); # Wesley Ivan Hurt, Feb 09 2014

Mathematica

Table[Binomial[n+2, 3]+Binomial[n, 3]+Binomial[n-1, 3], {n, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 11, 25}, 50] (* Harvey P. Dale, Jun 15 2011 *)

Prog

(PARI) a(n) = (n^3 - 2*n^2 + 5*n - 2)/2 \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Sequence in context: A115294 A110610 A051462 * A290876 A333643 A006522

Adjacent sequences: A006001 A006002 A006003 * A006005 A006006 A006007

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

Terms added by Wesley Ivan Hurt, Feb 09 2014

Status

approved