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A084155
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A Pell related fourth order recurrence.
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2
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0, 1, 4, 19, 88, 401, 1804, 8051, 35760, 158401, 700564, 3095731, 13673224, 60375953, 266559388, 1176763859, 5194762080, 22931453953, 101225940772, 446836798675, 1972442421688, 8706804701201, 38433749994028
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of A084154. a(n)=(A083878(n)-A001333(n))/2.
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FORMULA
| a(n)=8a(n-1)-18a(n-2)+8a(n-3)+7a(n-4), a(0)=0, a(1)=1, a(2)=4, a(3)=19; a(n)=((3+sqrt(2))^n+(3-sqrt(2))^n-(1+sqrt(2))^n-(1-sqrt(2))^n)/4; G.f.: x(1-4x+5x^2)/((1-2x-x^2)(1-6x+7x^2)); E.g.f. : exp(2x)sinh(x)cosh(sqrt(2)x).
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CROSSREFS
| Sequence in context: A180146 A017962 A192526 * A015530 A181880 A010907
Adjacent sequences: A084152 A084153 A084154 * A084156 A084157 A084158
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 16 2003
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EXTENSIONS
| Removed duplicate of g.f. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 22 2009
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