OFFSET
0,2
COMMENTS
The diagonal sums of number triangle A166335 are 1, 0, 3, 0, 11, 0, ...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Guo-Niu Han, Enumeration of Standard Puzzles, 2011. [Cached copy]
Guo-Niu Han, Enumeration of Standard Puzzles, arXiv:2006.14070 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (7,-17,17,-7,1).
FORMULA
G.f.: (1 - 4*x + 7*x^2 - 4*x^3 + x^4)/((1 - x)*(1 - 3*x + x^2)^2);
a(n) = 1 + 2*Sum{k=0..n} k*C(n + k, 2*k) = 1 + 2*Sum{k=0..n} (n-k)*C(2*n - k, k) = 1 + 2*A001870(n).
a(0) = 1, a(1) = 3, a(2) = 11, a(3) = 39, a(4) = 131, and a(n) = -17*a(n-1) + 17*a(n-2) - 7*a(n-3) + a(n-4) for n >= 4. - Harvey P. Dale, Jul 05 2014
MATHEMATICA
CoefficientList[Series[(1-4x+7x^2-4x^3+x^4)/(1-7x+17x^2-17x^3+7x^4-x^5), {x, 0, 30}], x] (* or *) LinearRecurrence[{7, -17, 17, -7, 1}, {1, 3, 11, 39, 131}, 30] (* Harvey P. Dale, Jul 05 2014 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Oct 12 2009
STATUS
approved