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A030118
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a(n) = a(n-1) - a(n-2) + n.
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0
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1, 1, 2, 4, 6, 7, 7, 7, 8, 10, 12, 13, 13, 13, 14, 16, 18, 19, 19, 19, 20, 22, 24, 25, 25, 25, 26, 28, 30, 31, 31, 31, 32, 34, 36, 37, 37, 37, 38, 40, 42, 43, 43, 43, 44, 46, 48, 49, 49, 49, 50, 52, 54, 55, 55, 55, 56, 58, 60, 61, 61, 61, 62, 64, 66, 67, 67, 67, 68, 70, 72, 73
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A130734-A010892 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
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FORMULA
| Periodic mod 6.
a(n)=(1/30)*{37*(n mod 6)+2*[(n+1) mod 6]-3*[(n+2) mod 6]-3*[(n+3) mod 6]+2*[(n+4) mod 6]+7*[(n+5) mod 6]}+6*sum{k=0..n}{1/3*(cos(2*Pi*k/3)+1/2)*(1+(-1)^k}-6, with n>=0. - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 01 2007
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MAPLE
| P:=proc(n) local a, i, k; for i from 0 by 1 to n do a:=1/30*(37*(i mod 6)+2*((i+1) mod 6)-3*((i+2) mod 6)-3*((i+3) mod 6)+2*((i+4) mod 6)+7*((i+5) mod 6))+6*sum('1/3*(cos(2*Pi*k/3)+1/2)*(1+(-1)^k)', 'k'=0..i)-6; print(a); od; end: P(100); - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 01 2007
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PROG
| (Other) sage: [lucas_number1(n, 2, 1)-lucas_number1(n-1, 1, 1) for n in xrange(1, 73)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
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CROSSREFS
| A130734, A010892 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 10 2009]
Sequence in context: A167689 A058184 A087777 * A023835 A174416 A138888
Adjacent sequences: A030115 A030116 A030117 * A030119 A030120 A030121
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KEYWORD
| nonn,easy
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AUTHOR
| Dragan Stevanovic (dragance(AT)ban.junis.ni.ac.yu)
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EXTENSIONS
| More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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