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A094686
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A Fibonacci convolution.
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8
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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; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| 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
| 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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MATHEMATICA
| a=0; b=0; lst={a, b}; Do[z=a+b+1; AppendTo[lst, z]; a=b; b=z; z=a+b-1; AppendTo[lst, z]; a=b; b=z; z=a+b; AppendTo[lst, z]; a=b; b=z, {n, 50}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 16 2010]
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CROSSREFS
| Sequence in context: A082222 A058630 A095092 * A095054 A032162 A000983
Adjacent sequences: A094683 A094684 A094685 * A094687 A094688 A094689
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 19 2004
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