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Search: id:A094686
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| A094686 |
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A Fibonacci convolution. |
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+0
9
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| 1, 0, 1, 2, 2, 4, 7, 10, 17, 28, 44, 72, 117, 188, 305, 494, 798, 1292, 2091, 3382, 5473, 8856, 14328, 23184, 37513, 60696, 98209, 158906, 257114, 416020, 673135, 1089154, 1762289, 2851444, 4613732, 7465176, 12078909, 19544084, 31622993, 51167078
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Convolution of A000045 and A049347.
Diagonal sums of number triangle A116088. - Paul Barry (pbarry(AT)wit.ie), Feb 04 2006
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FORMULA
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G.f. : 1/((1-x-x^2)(1+x+x^2)); a(n)=sum{k=0..n, Fib(k+1)2sqrt(3)cos(2*pi*(n-k)/3+pi/6)/3}; a(n)=a(n-2)+2a(n-3)+a(n-4).
a(n)=A005252(n)-(-cos(2*pi*n/3+pi/3)/2-sqrt(3)sin(2*pi*n/3+pi/3)/6+ sqrt(3)cos(pi*n/3+pi/6)/6+sin(pi*n/3+pi/6)/2); a(n)=sum{k=0..floor(n/2), if(mod(n-k, 2)=0, binomial(n-k, k), 0)}; a(n)=A093040(n-1)-Fib(n); - Paul Barry (pbarry(AT)wit.ie), Jan 13 2005
a(n)=sum{k=0..floor(n/2), C(n-k, k)(1+(-1)^(n-k))/2}; - Paul Barry (pbarry(AT)wit.ie), Sep 09 2005
a(n)=sum{k=0..floor(n/2), C(2k,n-2k)}=sum{k=0..floor(n/2), C(n-k,k)C(3k,n-k)/C(3k,k)}. - Paul Barry (pbarry(AT)wit.ie), Feb 04 2006
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CROSSREFS
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Sequence in context: A082222 A058630 A095092 this_sequence A095054 A032162 A000983
Adjacent sequences: A094683 A094684 A094685 this_sequence A094687 A094688 A094689
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 19 2004
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