A095934 Expansion of (1-x)^2/(1-5*x+3*x^2).

1, 3, 13, 56, 241, 1037, 4462, 19199, 82609, 355448, 1529413, 6580721, 28315366, 121834667, 524227237, 2255632184, 9705479209, 41760499493, 179686059838, 773148800711, 3326685824041, 14313982718072, 61589856118237, 265007332436969, 1140267093830134

Offset: 0

Author

N. J. A. Sloane, Jul 13 2004

Keywords

• nonn
• easy

Comments

a(n) is the number of generalized compositions of n when there are i+2 different types of i, (i=1,2,...). [Milan Janjic, Sep 24 2010]

Links

• P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102.
• P. J. Cameron, Some sequences of integers, in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.
• Index entries for linear recurrences with constant coefficients, signature (5,-3).

Crossrefs

Cf. A003480, A010903, A010920; equals A095939 + A095940.

Programs

Mathematica

CoefficientList[Series[(1-x)^2/(1-5x+3x^2),{x,0,30}],x] (* or *) LinearRecurrence[{5,-3},{1,3,13},30] (* Harvey P. Dale, Jun 21 2021 *)

PARI

a(n)=polcoeff((1-x)^2/(1-5*x+3*x^2)+x*O(x^n),n)

Formula

a(n+2) = 5a(n+1) - 3a(n) (n >= 1); a(0) = 1, a(1) = 3, a(2) = 13.