This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A114424 Number of partitions of n such that the size of the tail below the Durfee square is equal to the size of the tail to the right of the Durfee square. 1
 1, 0, 1, 1, 1, 1, 1, 4, 2, 4, 2, 9, 5, 9, 10, 17, 17, 17, 26, 29, 50, 34, 65, 61, 102, 72, 146, 130, 201, 170, 266, 289, 387, 388, 491, 611, 677, 811, 899, 1260, 1225, 1630, 1619, 2355, 2270, 3086, 2970, 4361, 4147, 5524, 5555, 7625, 7609, 9681, 10202, 13085 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 REFERENCES G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976 (pp. 27-28). G. E. Andrews and K. Eriksson, Integer Partitions, Cambridge Univ. Press, 2004 (pp. 75-78). LINKS Alois P. Heinz, Table of n, a(n) for n = 1..1000 FORMULA a(n) = coefficient of (t^0)(z^n) in G(t,1/t,z), where G(t,s,z)=sum(z^(k^2)/product((1-(tz)^j)(1-(sz)^j),j=1..k),k=1..infinity) is the trivariate g.f. according to partition size (z), size of the tail below the Durfee square (t) and size of the tail to the right of the Durfee square (s). EXAMPLE a(9) = 2 because we have [5,1,1,1,1] with both tails of size 4 and [3,3,3] with both tails of size 0. MAPLE g:=sum(z^(k^2)/product((1-(t*z)^j)*(1-(z/t)^j), j=1..k), k=1..10): gser:=simplify(series(g, z=0, 65)): 1, seq(coeff(numer(coeff(gser, z^n)), t^(n-1)), n=2..60); # second Maple program b:= proc(n, i) option remember;       `if`(n=0, 1, `if`(i<1, 0, b(n, i-1)+`if`(i>n, 0, b(n-i, i))))     end: a:= proc(n) local r; add (`if`(irem(n-d^2, 2, 'r')=1, 0,                            b(r, d)^2), d=1..floor(sqrt(n)))     end: seq (a(n), n=1..70); # Alois P. Heinz, Apr 09 2012 CROSSREFS Sequence in context: A147973 A010474 A064887 * A056158 A010316 A083954 Adjacent sequences:  A114421 A114422 A114423 * A114425 A114426 A114427 KEYWORD nonn AUTHOR Emeric Deutsch, Feb 12 2006 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .