A242499 Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 1.

1, 0, 1, 3, 1, 9, 11, 18, 51, 65, 151, 290, 477, 1043, 1835, 3486, 6931, 12540, 24607, 46797, 87979, 171072, 323269, 619245, 1190619, 2264925, 4357211, 8343322, 15973309, 30711853, 58846191, 113027716, 217192103, 416964202, 801880039, 1541412015, 2963997227

Offset

1,4

Comments

With offset 2 number of compositions of n, where the difference between the number of odd parts and the number of even parts is -1.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Formula

Recurrence (for n>=5): (n+2)*(16*n^4 - 128*n^3 + 344*n^2 - 352*n + 89)*a(n) = -32*(n+1)*(2*n-5)*a(n-1) + 2*(16*n^5 - 112*n^4 + 264*n^3 - 320*n^2 + 301*n - 89)*a(n-2) + 2*(2*n-5)*(16*n^4 - 80*n^3 + 80*n^2 + 36*n - 53)*a(n-3) - (n-4)*(16*n^4 - 64*n^3 + 56*n^2 + 16*n - 31)*a(n-4). - Vaclav Kotesovec, May 20 2014

Maple

a:= proc(n) option remember;
      `if`(n<6, [0, 1, 0, 1, 3, 1][n+1],
      ((3*n-2)*a(n-2) +(4*n+2)*a(n-3) -(3*n-10)*a(n-4)
       -(4*n-22)*a(n-5) +(n-6)*a(n-6))/(n+2))
    end:
seq(a(n), n=1..50);

Mathematica

a[n_] := a[n] = If[n<6, {0, 1, 0, 1, 3, 1}[[n+1]], ((3n-2)a[n-2] + (4n+2)a[n-3] - (3n-10)a[n-4] - (4n-22)a[n-5] + (n-6)a[n-6])/(n+2)];
Array[a, 50] (* Jean-François Alcover, Dec 28 2020, after Alois P. Heinz *)

Crossrefs

Column k=1 of A242498.

Sequence in context: A184061 A222057 A260285 * A354622 A173020 A334062

Adjacent sequences: A242496 A242497 A242498 * A242500 A242501 A242502

Keyword

nonn

Author

Alois P. Heinz, May 16 2014

Status

approved