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A027660
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C(n+2,2)+C(n+2,3)+C(n+2,4)+C(n+2,5).
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2
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1, 4, 11, 26, 56, 112, 210, 372, 627, 1012, 1573, 2366, 3458, 4928, 6868, 9384, 12597, 16644, 21679, 27874, 35420, 44528, 55430, 68380, 83655, 101556, 122409, 146566, 174406, 206336, 242792
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also, number of 135246-avoiding permutations of n+2 with exactly 1 descent. E.g. there are 57 permutations of 6 with exactly 1 descent. Of these, only the permutation 135246 contains the pattern 135246 so a(4)=56. - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 29 2004
If Y is a 2-subset of an n-set X then, for n>=5, a(n-5) is the number of 5-subsets of X which have no exactly one element in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
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LINKS
| Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
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FORMULA
| G.f.: (1-2x+2x^2)/(1-x)^6. - Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Nov 29 2004
binomial(n,5)+binomial(n,3), n>=3. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006
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MAPLE
| (1/120)*(n+3)*(n+2)*(n+1)*(n^2-n+20);
[seq(binomial(n, 5)+binomial(n, 3), n=3..34)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006
seq(sum(binomial(n, k+1), k=1..4), n=2..32); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2007
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MATHEMATICA
| a=1; b=2; c=3; s=4; lst={a, s}; Do[a+=n; b+=a; c+=b; s+=c; AppendTo[lst, s], {n, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 24 2009]
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PROG
| (Other) sage: [binomial(n, 2)+binomial(n, 3)+binomial(n, 4)+binomial(n, 5) for n in xrange(2, 33)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 17 2009]
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CROSSREFS
| Cf. A000295.
Sequence in context: A027966 A141534 A192961 * A002940 A030196 A125128
Adjacent sequences: A027657 A027658 A027659 * A027661 A027662 A027663
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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