OFFSET
1,1
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
V. J. W. Guo and J. Zeng, The number of convex polyominoes and the generating function of Jacobi polynomials, arXiv:math/0403262 [math.CO], 2004.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = ((3*n+2)*C(2n+4, 4) - 4*n*C(n+2, n)^2)/(n+2), n>0.
a(n) = (6*n^4 + 20*n^3 + 27*n^2 + 19*n + 6)/6.
From Colin Barker, Feb 24 2019: (Start)
G.f.: x*(13 + 3*x + 12*x^2 - 5*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
E.g.f.: -1 + (6 + 72*x + 129*x^2 + 56*x^3 + 6*x^4)*exp(x)/6. - G. C. Greubel, Jun 26 2019
MATHEMATICA
a[n_] := n^4 + 10*n^3/3 + 9*n^2/2 + 19*n/6 + 1; Array[a, 40] (* Jean-François Alcover, Feb 24 2019 *)
PROG
(PARI) Vec(x*(13 + 3*x + 12*x^2 - 5*x^3 + x^4) / (1 - x)^5 + O(x^40)) \\ Colin Barker, Feb 24 2019
(Magma) [(6*n^4 + 20*n^3 + 27*n^2 + 19*n + 6)/6: n in [1..40]]; // G. C. Greubel, Jun 26 2019
(Sage) [(6*n^4 + 20*n^3 + 27*n^2 + 19*n + 6)/6 for n in (1..40)] # G. C. Greubel, Jun 26 2019
(GAP) List([1..40], n-> (6*n^4 + 20*n^3 + 27*n^2 + 19*n + 6)/6) # G. C. Greubel, Jun 26 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Mar 21 2004
STATUS
approved