OFFSET
0,2
COMMENTS
The end values of the partial rows on the main diagonal of A332662 in the representation in the example section.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
FORMULA
a(n) = [x^n] (x*(x^2 + x + 6))/(x - 1)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = binomial(n+2, 3) + binomial(n+1, 3) + 2*(n+1)*binomial(n+1, 2) + binomial(n, 1) = A331987(n) + n.
MAPLE
a := n -> (8*n^3 + 15*n^2 + 13*n)/6: seq(a(n), n=0..41);
gf := (x*(x^2 + x + 6))/(x - 1)^4: ser := series(gf, x, 44):
seq(coeff(ser, x, n), n=0..41);
MATHEMATICA
LinearRecurrence[{4, -6, 4, -1}, {0, 6, 25, 65}, 42]
Table[(8n^3+15n^2+13n)/6, {n, 0, 50}] (* Harvey P. Dale, Sep 13 2024 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Feb 20 2020
STATUS
approved