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A144044
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((1+sqrt11)^n-(1-sqrt11)^n)^2/44
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0
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1, 4, 196, 2304, 55696, 906304, 18181696, 325730304, 6199357696, 114211554304, 2141141533696, 39766241378304, 742275639709696, 13817991215202304, 257604225193885696, 4798702283133026304, 89428432275804061696
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Sequences of the form a(n) = ((A+sqrt B)^n-(A-sqrt B)^n)^2/(4B) have recurrences a(n) = (3A^2+B) *a(n-1) +(B+3A^2)*(B-A^2) *a(n-2) -(B-A^2)^3*a(n-3) and generating functions x(1+(A^2-B)x) / ((1 -(A^2-B)x)(1-2(A^2+B)x +(A^4-2A^2B+B^2)x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 01 2008]
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FORMULA
| a(n)=14*a(n-1)+140*a(n-2)-1000*a(n-3). G.f. x(1-10x)/((10x+1)(1-24x+100x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 01 2008]
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EXAMPLE
| a(3) = 196
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CROSSREFS
| Sequence in context: A028370 A042127 A017546 * A180991 A065246 A156235
Adjacent sequences: A144041 A144042 A144043 * A144045 A144046 A144047
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Sep 08 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 01 2008
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