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Search: id:A050228
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| A050228 |
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a(n) is the number of subsequences {s(k)} of {1,2,3,...n} such that s(k+1)-s(k) is 1 or 3. |
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+0
2
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| 1, 3, 6, 11, 19, 31, 49, 76, 116, 175, 262, 390, 578, 854, 1259, 1853, 2724, 4001, 5873, 8617, 12639, 18534, 27174, 39837, 58396, 85596, 125460, 183884, 269509, 394999, 578914, 848455, 1243487, 1822435, 2670925, 3914448, 5736920, 8407883
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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The second differences c(n) of {a(n)} satisfy c(n)=c(n-1)+c(n-3) and give A000930 with the first 5 terms deleted.
Partial sums of A077868. - Paul Barry (pbarry(AT)wit.ie), Sep 16 2004
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FORMULA
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G.f. : x/((1-x)^3-x^3(1-x)^2); a(n)=3a(n-1)-3a(n-2)+2a(n-3)-2a(n-4)+a(n-5); a(n-1)=sum{k=0..floor(n/3), binomial(n-2k, k+2)}. - Paul Barry (pbarry(AT)wit.ie), Sep 16 2004
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MAPLE
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with(combstruct): SubSetSeqU := [T, {T=Subst(U, U), S=Set(U, card>=3), U=Sequence(Z, card>=3)}, unlabeled]: seq(count(SubSetSeqU, size=n), n=9..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 18 2008
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CROSSREFS
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Adjacent sequences: A050225 A050226 A050227 this_sequence A050229 A050230 A050231
Sequence in context: A091094 A116100 A004133 this_sequence A114089 A001976 A144115
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Dec 20 1999
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