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Search: id:A022097
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| A022097 |
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Fibonacci sequence beginning 1 7. |
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+0
11
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| 1, 7, 8, 15, 23, 38, 61, 99, 160, 259, 419, 678, 1097, 1775, 2872, 4647, 7519, 12166, 19685, 31851, 51536, 83387, 134923, 218310, 353233, 571543, 924776, 1496319, 2421095, 3917414, 6338509, 10255923
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n-1)=sum(P(7;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=6. These are the SW-NE diagonals in P(7;n,k), the (7,1) Pascal triangle A093564. Observation by Paul Barry (pbarry(AT)wit.ie, Apr 29 2004. Proof via recursion relations and comparison of inputs.
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LINKS
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Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=7. a(-1):=6.
G.f.: (1+6*x)/(1-x-x^2).
Row sums of triangle A131778 starting (1, 7, 8, 15, 23, 38,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 14 2007
a(n)=((1+sqrt5)^n-(1-sqrt5)^n)/(2^n*sqrt5)+ 3*((1+sqrt5)^(n-1)-(1-sqrt5)^(n-1))/(2^(n-2)*sqrt5). Offset 1. a(3)=8. [From Al Hakanson (hawkuu(AT)gmail.com), Jan 14 2009, corrected Jan 17 2009]
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MATHEMATICA
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a={}; b=1; c=7; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (Vladimir Orlovsky, Jul 22 2008)
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CROSSREFS
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a(n) = A101220(6, 0, n+1).
a(n) = A109754(6, n+1).
a(k) = A118654(3, k).
Cf. A131778.
Sequence in context: A165465 A047521 A070424 this_sequence A041100 A129658 A041693
Adjacent sequences: A022094 A022095 A022096 this_sequence A022098 A022099 A022100
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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