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 A316403 Number of multisets of exactly two nonempty binary words with a total of n letters such that no word has a majority of 0's. 2
 1, 3, 10, 23, 59, 134, 320, 699, 1599, 3434, 7682, 16246, 35762, 74892, 163032, 338771, 731051, 1510466, 3237206, 6658530, 14189790, 29083988, 61687496, 126076638, 266332390, 543061284, 1143207236, 2326521164, 4882706596, 9920514328, 20764519984, 42130081155 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 2..1000 FORMULA a(n) = [x^n y^2] 1/Product_{j>=1} (1-y*x^j)^A027306(j). EXAMPLE a(4) = 10: {1,011}, {1,101}, {1,110}, {1,111}, {01,01}, {01,10}, {01,11}, {10,10}, {10,11}, {11,11}. a(5) = 23: {1,0011}, {1,0101}, {1,0110}, {1,0111}, {1,1001}, {1,1010}, {1,1011}, {1,1100}, {1,1101}, {1,1110}, {1,1111}, {01,011}, {01,101}, {01,110}, {01,111}, {10,011}, {10,101}, {10,110}, {10,111}, {11,011}, {11,101}, {11,110}, {11,111}. MAPLE 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, 3) end: a:= n-> coeff(b(n\$2), x, 2): seq(a(n), n=2..33); CROSSREFS Column k=2 of A292506. Cf. A027306, A292549. Sequence in context: A080204 A115982 A167243 * A185828 A134438 A092255 Adjacent sequences: A316400 A316401 A316402 * A316404 A316405 A316406 KEYWORD nonn AUTHOR Alois P. Heinz, Jul 02 2018 STATUS approved

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Last modified February 27 14:08 EST 2024. Contains 370375 sequences. (Running on oeis4.)