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Search: id:A054469
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| A054469 |
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A second order recursive sequence. |
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+0
3
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| 1, 7, 28, 85, 218, 499, 1053, 2092, 3970, 7272, 12958, 22596, 38739, 65535, 109714, 182185, 300620, 493635, 807555, 1317360, 2144396, 3485032, 5657028, 9174560, 14869613, 24088399, 39009168, 63156437, 102233030, 165466347, 267786673
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
A. F. Horadam,Special Properties of the Sequence W(n){a,b; p,q}, Fib.Quart., Vol. 5,No.5(1967), pps. 424-434.
A. K. Whitford, Binet's Formula Generalized, Fib. Quart., Vol. 15, No. 1(1977), pps. 21, 24, 29.
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FORMULA
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a(n)=a(n-1)+a(n-2)+(n+2)*C(n+3, 3)/2=a(n-1)+a(n-2)+(n+1)(n+2)^2(n+3)/12; a(-n)=0.
a(n)=sum{C(n+5-i, n+2-2i); i=1 to [(n+2)/2]}+2*sum{C(n+5-i, n+1-2i); i=1 to [(n+1)/2]; where [x]=greatest integer in x.
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CROSSREFS
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Cf. A001891 and A001911.
Right-hand column 11 of triangle A011794.
Sequence in context: A023032 A000579 A049017 this_sequence A117473 A022572 A024207
Adjacent sequences: A054466 A054467 A054468 this_sequence A054470 A054471 A054472
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Mar 31 2000
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