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A174247 Number of words of length n composed of the letters a, b, and c with at least as many a's as b's, and at least as many b's as c's, and no a's adjacent. 1
1, 1, 2, 7, 9, 21, 76, 104, 255, 936, 1321, 3327, 12250, 17682, 45200, 166420, 244431, 630586, 2318863, 3453662, 8964527, 32909250, 49579091, 129250365, 473604092, 720390529, 1884080667, 6890849851, 10567693128, 27706723888, 101151927464, 156225285080, 410396361463 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..500

FORMULA

a(n) = Sum_{i=floor((n+2)/3)..floor((n+1)/2)} Sum_{j=floor((n-i+1)/2)..min(n-i, i)} binomial(n-i+1, i)*binomial(n-i, j). - Andrew Howroyd, Jan 07 2020, after Maple

EXAMPLE

For n = 0, there is 1 word (the empty word).

For n = 1, there is 1 word: a.

For n = 2, there are 2 words: ab, ba.

For n = 3, there are 7 words: aba, abc, acb, bac, bca, cab, cba.

MAPLE

myseq:=n->add(add(binomial(n-na+1, na)*binomial(n-na, nb), nb=floor((n-na+1)/2)..min(n-na, na)), na=floor((n+2)/3)..floor((n+1)/2));

PROG

(PARI) a(n)={sum(i=(n+2)\3, (n+1)\2, sum(j=(n-i+1)\2, min(n-i, i), binomial(n-i+1, i)*binomial(n-i, j)))} \\ Andrew Howroyd, Jan 07 2020

CROSSREFS

Sequence in context: A293645 A293646 A020895 * A321322 A065139 A093916

Adjacent sequences:  A174244 A174245 A174246 * A174248 A174249 A174250

KEYWORD

nonn,easy

AUTHOR

Amanda Lee (amanda.lee(AT)dpcdsb.org), Mar 13 2010

EXTENSIONS

Terms a(11) and beyond from Andrew Howroyd, Jan 07 2020

STATUS

approved

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Last modified September 21 10:03 EDT 2020. Contains 337268 sequences. (Running on oeis4.)