OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Ping Sun, Proof of two conjectures of Petkovsek and Wilf on Gessel walks Discrete Math. 312 (2012), no. 24, 3649--3655. MR2979494. See Th. 1.2, case 3.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
G.f.: (11-18*x+12*x^2-3*x^3)/(1-x)^5. - Vincenzo Librandi, Dec 12 2014
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) n>4. - Vincenzo Librandi, Dec 12 2014
MATHEMATICA
Table[(n + 1) (n^3 + 15 n^2 + 74 n + 132) / 12, {n, 0, 50}] (* or *) CoefficientList[Series[(11 - 18 x + 12 x^2 - 3 x^3) / (1 - x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 12 2014 *)
PROG
(Maxima) A217947(n):=(n+1)*(n^3+15*n^2+74*n+132)/12$
makelist(A217947(n), n, 0, 30); /* Martin Ettl, Nov 08 2012 */
(Magma) [(n+1)*(n^3+15*n^2+74*n+132)/12: n in [0..50]] /* or */ I:=[11, 37, 87, 172, 305]; [n le 5 select I[n] else 5*Self(n-1)-10*Self(n-2)+10*Self(n-3)-5*Self(n-4)+Self(n-5): n in [1..50]] ; // Vincenzo Librandi, Dec 12 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 07 2012
STATUS
approved