

A011863


Nearest integer to (n/2)^4.


15



0, 0, 1, 5, 16, 39, 81, 150, 256, 410, 625, 915, 1296, 1785, 2401, 3164, 4096, 5220, 6561, 8145, 10000, 12155, 14641, 17490, 20736, 24414, 28561, 33215, 38416, 44205, 50625, 57720, 65536, 74120, 83521, 93789, 104976, 117135, 130321, 144590
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,4


COMMENTS

Number of ways to put n1 copies of 1,2,3 into sets. [Zeilberger?]
s(n) is the number of 4tuples (w,x,y,z) with all terms in {1,...,n} and wx >= w + yz; see A186707.  Clark Kimberling, May 24 2012


LINKS



FORMULA

G.f.: x^2*(1 + x + x^2)/((1  x)^5*(1+x)).
a(n) = +4*a(n1) 5*a(n2) +5*a(n4) 4*a(n5) +a(n6).  R. J. Mathar, Dec 07 2010
n*(n^2+n+2)*a(n+1) = 4*(n^2+2*n+2)*a(n)+(n+2)*(n^2+3*n+4)*a(n1). Holonomic Ansatz with smallest order of recurrence.  Thotsaporn Thanatipanonda, Dec 12 2010
E.g.f.: (1/32)*exp(x)*(1 + exp(2*x)*(1 + 2*x + 14*x^2 + 12*x^3 + 2*x^4)).  Stefano Spezia, Dec 29 2019
Sum_{n>=2} 1/a(n) = 6 + Pi^4/90  2*Pi*tanh(Pi/2).  Amiram Eldar, Aug 13 2022


MAPLE

seq(round((n/2)^4), n=0..40);


MATHEMATICA

Round[(Range[40]/2)^4] (* or *) LinearRecurrence[{4, 5, 0, 5, 4, 1}, {0, 1, 5, 16, 39, 81}, 40] (* Harvey P. Dale, Feb 07 2015 *)


PROG

(Magma) [ (2*n^4(1(1)^n))/32: n in [0..50] ];


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS

Missing a(0) added by N. J. A. Sloane, Dec 29 2019. As a result some of the comments and formulas will need to be adjusted.


STATUS

approved



