A261857
Number of compositions of n into distinct parts where each part i is marked with a word of length i over a senary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
Original entry on oeis.org
403, 3090, 26523, 178456, 4328268, 11655792, 55380132, 203857488, 908020203, 15089942326, 32659354659, 119798424120, 366557119686, 1229877368940, 4069268482608, 64750089252368, 122070519766665, 408439013722194, 1090232738714433, 3275624230408044
Offset: 6
-
b:= proc(n, i, p, k) option remember;
`if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(6):
seq(a(n), n=6..30);
A261859
Number of compositions of n into distinct parts where each part i is marked with a word of length i over an octonary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
Original entry on oeis.org
2873, 66904, 4351388, 20331080, 157483354, 901563512, 6174438308, 180660353288, 511805155863, 2507827775824, 10089884785056, 44796664928048, 200977872433624, 5149800722642960, 11741438872834432, 48645418597510928, 159659060979170671, 593940633500376248
Offset: 8
-
b:= proc(n, i, p, k) option remember;
`if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(8):
seq(a(n), n=8..30);
A261860
Number of compositions of n into distinct parts where each part i is marked with a word of length i over a nonary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
Original entry on oeis.org
12607, 1850013, 13188465, 141059073, 1056825045, 9244127655, 358616974839, 1185100976313, 6776480736882, 31512728488918, 161603593094034, 844675656403032, 26805281002135578, 67485379090772970, 310715577607315770, 1129828504295753862, 4665897718158585321
Offset: 9
-
b:= proc(n, i, p, k) option remember;
`if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(9):
seq(a(n), n=9..30);
A261861
Number of compositions of n into distinct parts where each part i is marked with a word of length i over a denary alphabet whose letters appear in alphabetical order and all letters occur at least once in the composition.
Original entry on oeis.org
333051, 4822430, 79871395, 832560780, 9644631215, 503145835150, 1977105518235, 13353202808060, 72444344358890, 431802346970780, 2638310862477610, 102808411342614000, 286995037461236030, 1470656290936993540, 5931973064021096010, 27203387338778029760
Offset: 10
-
b:= proc(n, i, p, k) option remember;
`if`(i*(i+1)/2n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
end:
a:= n->(k->add(b(n$2, 0, k-i)*(-1)^i*binomial(k, i), i=0..k))(10):
seq(a(n), n=10..30);
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