OFFSET
0,2
COMMENTS
Binomial transform yields 1,12,23,12,0,0,0,0,0,0,.. - R. J. Mathar, Apr 21 2008
REFERENCES
J. H. Conway and R. K. Guy, The Book of Numbers, p. 83.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
M. E. Larsen, The eternal triangle - a history of a counting problem, College Math. J., 20 (1989), 370-392.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: (1 + 9*x + 2*x^2) / (1-x)^4. - R. J. Mathar, Apr 21 2008
From G. C. Greubel, Oct 29 2016: (Start)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
E.g.f.: (1/2)*(2 + 24*x + 23*x^2 + 4*x^3)*exp(x). (End)
a(n) = ((2*n+1)*(2*n+3)*(4*n+3) - 1)/8 = (n+1)*(4*n^2 + 7*n + 2)/2, for n >= 0. See the Conway and Guy reference. - Wolfdieter Lang, Apr 16 2020
MATHEMATICA
Table[(4*n^3 + 11*n^2 + 9*n + 2)/2, {n, 0, 25}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 13, 48, 118}, 25] (* G. C. Greubel, Oct 29 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 05 2008
STATUS
approved