OFFSET
0,1
LINKS
Stefano Spezia, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: (6-3*x-3*x^2+x^3)/(1-x)^4. - Vincenzo Librandi, Dec 14 2014
E.g.f.: exp(x)*(36 + 90*x + 27*x^2 + x^3)/6. - Stefano Spezia, May 30 2023
EXAMPLE
a(0)=A=6; a(1)=a(0)+(A+1)+(A+2)=3A+3, a(2)=a(1)+(A+1)+(A+2)+(A+3)=6A+9, a(3)=a(2)+(A+1)+(A+2)+(A+3)+(A+4)=10A+19, ...
MATHEMATICA
Table[(n^3+24n^2+65n+36)/6, {n, 0, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {6, 21, 45, 79}, 50] (* Harvey P. Dale, Dec 15 2014 *)
CoefficientList[Series[(6 - 3 x - 3 x^2 + x^3) / (1 - x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Dec 16 2014 *)
PROG
(PARI) a(n) = (n^3+24*n^2+65*n+36)/6; \\ Michel Marcus, Aug 24 2013
(Magma) [(n^3+24*n^2+65*n+36)/6: n in [0..40]]; // Vincenzo Librandi, Dec 16 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Helmut E. Fuchs (helmut2(AT)juno.com), Oct 26 2003
EXTENSIONS
New definition from Vladeta Jovovic, Oct 27 2003
More terms from Ray Chandler, Oct 27 2003
STATUS
approved