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Search: id:A079289
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| A079289 |
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For even n, a(n)=a(n-2)+a(n-1)+2^(n/2-2), n>2. For odd n, a(n)=a(n-2)+a(n-1) |
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+0
1
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| 1, 1, 2, 3, 6, 9, 17, 26, 47, 73, 128, 201, 345, 546, 923, 1469, 2456, 3925, 6509, 10434, 17199, 27633, 45344, 72977, 119345, 192322, 313715, 506037, 823848, 1329885, 2161925, 3491810, 5670119, 9161929, 14864816, 24026745, 38957097, 62983842
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Generalized Fibonacci sequence related to partial row sum triangles based on Pascal's triangle.
Call a multiset of nonzero integers good if the sum of the cubes is the square of the sum. The number of ascending chains of good multisets starting from the empty set by adding one element at a time is a(n). - Michael Somos Apr 14 2005.
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FORMULA
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a(n)=a(n-2)+a(n-1)+floor(2^(k/2-2))(1-(-1)^(k+1))/2
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EXAMPLE
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a(4)=6 from the good multisets {-1,-1,1,1},{-1,1,1,2},{-2,-1,1,2},{-2,1,2,2},{-3,1,2,3},{1,2,3,4}.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<3, (n>=0)+(n>1), A=vector(n, i, i); for(i=3, n, A[i]=A[i-1]+A[i-2]+ if(i%2==0, 2^(i/2-2))); A[n])} /* Michael Somos Apr 14 2005 */
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CROSSREFS
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Sequence in context: A056768 A029511 A056532 this_sequence A048811 A142155 A092351
Adjacent sequences: A079286 A079287 A079288 this_sequence A079290 A079291 A079292
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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), Feb 08 2003
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