A316409
Number of multisets of exactly eight nonempty binary words with a total of n letters such that no word has a majority of 0's.
Original entry on oeis.org
1, 3, 10, 33, 98, 291, 826, 2320, 6342, 17133, 45504, 119580, 310416, 798196, 2033289, 5136803, 12878647, 32056022, 79277444, 194822462, 476101571, 1156995495, 2797803485, 6731961588, 16126628466, 38459836055, 91355046531, 216126089962, 509445131238
Offset: 8
-
g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 9)
end:
a:= n-> coeff(b(n$2), x, 8):
seq(a(n), n=8..36);
A316410
Number of multisets of exactly nine nonempty binary words with a total of n letters such that no word has a majority of 0's.
Original entry on oeis.org
1, 3, 10, 33, 98, 291, 826, 2320, 6342, 17188, 45684, 120435, 313280, 808581, 2065885, 5241557, 13191343, 32992806, 81964072, 202499115, 497418503, 1215823396, 2956890329, 7159215090, 17256728038, 41428552721, 99060756883, 235997525351, 560191343126
Offset: 9
-
g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 10)
end:
a:= n-> coeff(b(n$2), x, 9):
seq(a(n), n=9..37);
A316411
Number of multisets of exactly ten nonempty binary words with a total of n letters such that no word has a majority of 0's.
Original entry on oeis.org
1, 3, 10, 33, 98, 291, 826, 2320, 6342, 17188, 45750, 120655, 314335, 812161, 2078985, 5283157, 13326283, 33400066, 83195864, 206069915, 507722068, 1244740868, 3037497201, 7379529734, 17854498058, 43026654989, 103302756909, 247127149283, 589196413579
Offset: 10
-
g:= n-> 2^(n-1)+`if`(n::odd, 0, binomial(n, n/2)/2):
b:= proc(n, i) option remember; series(`if`(n=0 or i=1, x^n, add(
binomial(g(i)+j-1, j)*b(n-i*j, i-1)*x^j, j=0..n/i)), x, 11)
end:
a:= n-> coeff(b(n$2), x, 10):
seq(a(n), n=10..38);