OFFSET
0,2
COMMENTS
Essentially the same as A049611.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Igor Makhlin, Gröbner fans of Hibi ideals, generalized Hibi ideals and flag varieties, arXiv:2003.02916 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
FORMULA
G.f.: (1 - x)^2/(1 - 2*x)^3.
a(n) = (n^2 + 7*n + 8)*2^(n - 3).
a(n) = Sum_{k=0..n} C(n, k)*C(k+2, 2).
a(n) = A049611(n+1).
EXAMPLE
From Bruno Berselli, Jul 17 2018: (Start)
Let the triangle:
1
3, 4
6, 9, 13
10, 16, 25, 38
15, 25, 41, 66, 104
21, 36, 61, 102, 168, 272
28, 49, 85, 146, 248, 416, 688
36, 64, 113, 198, 344, 592, 1008, 1696, etc.
where the first column is A000217 (without 0). The other terms are calculated with the recurrence T(r, c) = T(r-1, c-1) + T(r, c-1).
The sequence is the right side of the triangle.
(End)
MAPLE
a := n -> hypergeom([-n, 3], [1], -1);
seq(round(evalf(a(n), 32)), n=0..31); # Peter Luschny, Aug 02 2014
MATHEMATICA
CoefficientList[ Series[(1 - x)^2/(1 - 2 x)^3, {x, 0, 28}], x] (* Robert G. Wilson v, Jun 28 2005 *)
LinearRecurrence[{6, -12, 8}, {1, 4, 13}, 30] (* Harvey P. Dale, Aug 05 2019 *)
PROG
(Magma) [(n^2+7*n+8)*2^(n-3): n in [0..40]]; // Vincenzo Librandi, Aug 03 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Jun 09 2003
STATUS
approved