OFFSET
0,3
COMMENTS
For a guide to related sequences, see A211795.
For n>=1, a(n) is the n-th antidiagonal sums of the convolution array A213831. - Clark Kimberling, Jul 04 2012
LINKS
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
a(n) = (n + 2*n^3 + 3*n^4)/6. - Clark Kimberling, Jul 10 2012
G.f.: x*(1 + x)*(1 + 5*x)/(1 - x)^5. - Clark Kimberling, Jul 10 2012
a(n) = Sum_{k=0..n} A059722(k). - J. M. Bergot, Nov 02 2012
MATHEMATICA
t = Compile[{{n, _Integer}}, Module[{s = 0},
(Do[If[w + x <= y + z, s = s + 1],
{w, 1, #}, {x, 1, #}, {y, 1, #}, {z, 1, #}] &[n]; s)]];
Map[t[#] &, Range[0, 40]] (* A212560 *)
PROG
(PARI) a(n)=(n+2*n^3+3*n^4)/6 \\ Charles R Greathouse IV, Oct 21 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 21 2012
STATUS
approved