A261842 Number of compositions of n into distinct parts where each part i is marked with a word of length i over a quaternary alphabet whose letters appear in alphabetical order.

1, 4, 10, 100, 195, 736, 6032, 11712, 35285, 100260, 871386, 1492820, 4438573, 10525720, 29825140, 241360728, 405645867, 1086289116, 2489722574, 6158961820, 14573822743, 123303661384, 192326074572, 504783599080, 1073240557055, 2539006453740, 5337585654950

Offset: 0

Author

Alois P. Heinz, Sep 03 2015

Keywords

• nonn

Comments

Also matrices with four rows of nonnegative integers with distinct positive column sums and total element sum n.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000

Crossrefs

Column k=4 of A261835.

Programs

Maple

b:= proc(n, i, p) option remember;
      `if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1)*binomial(i+3, 3))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..40);