This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A218355 Number of partitions into distinct parts where all differences between consecutive parts are odd and the minimal part is even. 3
 1, 0, 1, 0, 1, 1, 1, 1, 1, 3, 1, 3, 1, 5, 2, 6, 2, 8, 3, 9, 5, 12, 7, 13, 9, 16, 13, 19, 17, 22, 23, 25, 29, 30, 37, 35, 46, 41, 58, 49, 70, 57, 85, 68, 103, 81, 123, 97, 145, 115, 172, 139, 201, 164, 236, 197, 274, 234, 318, 280, 368, 330, 425, 394, 488, 463, 561, 548, 644, 642, 738, 755, 844, 879, 965, 1029 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS Parts are even, odd, even, odd, ... . LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 FORMULA G.f.: sum(n>=0, x^((n+1)*(n+4)/2) / prod(k=1..n+1, 1-x^(2*k) ) ). a(n) = A179080(n) - A179049(n). EXAMPLE The a(23) = 13 such partitions of 23 are: [ 1]  2 3 18 [ 2]  2 5 16 [ 3]  2 7 14 [ 4]  2 9 12 [ 5]  2 21 [ 6]  4 5 14 [ 7]  4 7 12 [ 8]  4 9 10 [ 9]  4 19 [10]  6 7 10 [11]  6 17 [12]  8 15 [13]  10 13 MAPLE b:= proc(n, i, t) option remember; `if`(n=0, 1-irem(t, 2),       `if`(i<1, 0, b(n, i-1, t)+`if`(i<=n and irem(i, 2)<>t,        b(n-i, i-1, irem(i, 2)), 0)))     end: a:= n-> `if`(n=0, 1, add(b(n-i, i-1, irem(i, 2)), i=1..n)): seq(a(n), n=0..100);  # Alois P. Heinz, Nov 08 2012 MATHEMATICA b[n_, i_, t_] := b[n, i, t] = If[n==0, 1-Mod[t, 2], If[i<1, 0, b[n, i-1, t] + If[i <= n && Mod[i, 2] != t, b[n-i, i-1, Mod[i, 2]], 0]]]; a[n_] := If[n==0, 1, Sum[ b[n-i, i-1, Mod[i, 2]], {i, 1, n}]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jul 02 2015, after Alois P. Heinz *) PROG (PARI) N=76; x='x+O('x^N); gf179080 = sum(n=0, N, x^(n*(n+1)/2) / prod(k=1, n+1, 1-x^(2*k) ) ); gf179049 = sum(n=0, N, x^(n*(n+1)/2) / prod(k=1, n, 1-x^(2*k) ) ); gf = gf179080 - gf179049; Vec( gf ) (PARI) N=75; x='x+O('x^N); gf = sum(n=0, N, x^((n+1)*(n+4)/2) / prod(k=1, n+1, 1-x^(2*k) ) ); v2=Vec( gf ) CROSSREFS Cf. A179049 (parts are odd, even, odd, even, ...). Sequence in context: A293485 A250207 A216319 * A103790 A249947 A193583 Adjacent sequences:  A218352 A218353 A218354 * A218356 A218357 A218358 KEYWORD nonn AUTHOR Joerg Arndt, Oct 27 2012 STATUS approved

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