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Search: id:A081568
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| A081568 |
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Third binomial transform of F(n+1). |
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+0
4
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| 1, 4, 17, 75, 338, 1541, 7069, 32532, 149965, 691903, 3193706, 14745009, 68084297, 314394980, 1451837593, 6704518371, 30961415074, 142980203437, 660285858245, 3049218769908, 14081386948661, 65028302171639, 300302858766202
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A081567. Case k=3 of family of recurrences a(n)=(2k+1)a(n-1)-A028387(k-1)a(n-2), a(0)=1,a(1)=k+1.
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FORMULA
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a(n)=7a(n-1)-11a(n-2), a(0)=1, a(1)=4. a(n)=(1/2 - sqrt(5)/10)(7/2 - sqrt(5)/2)^n + (sqrt(5)/10 + 1/2)(sqrt(5)/2 + 7/2)^n G.f.: (1-3x)/(1-7x+11x^2).
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CROSSREFS
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Cf. A000045.
Sequence in context: A086351 A049027 A026751 this_sequence A026378 A151247 A117439
Adjacent sequences: A081565 A081566 A081567 this_sequence A081569 A081570 A081571
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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), Mar 22 2003
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