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Search: id:A053404
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| A053404 |
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A second order recurrence. |
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+0
10
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| 1, 1, 13, 25, 181, 481, 2653, 8425, 40261, 141361, 624493, 2320825, 9814741, 37664641, 155441533, 607417225, 2472715621, 9761722321, 39434309773, 156574977625, 629786694901, 2508686426401, 10066126765213, 40170363882025
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Hankel transform is := 1,12,0,0,0,0,0,0,0,0,0,0,... [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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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. K. Whitford, Binet's Formula Generalized, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21,24,29.
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FORMULA
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a(n)=[(4^(n+1))-(-3)^(n+1)]/7. a(n)=a(n-1)+12a(n-2), n>1; a(0)=1, a(1)=1.
Convolution of 4^n and (-3)^n. G.f. : 1/((1+3x)(1-4x)); a(n)=sum{k=0..n, 4^k*(-3)^(n-k)}=sum{k=0..n, (-3)^k*4^(n-k)}; - Paul Barry (pbarry(AT)wit.ie), Jul 30 2004
a(n)=Sum_{k, 0<=k<=n} A109466(n,k)*(-12)^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 26 2008]
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PROGRAM
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(Other) sage: [lucas_number1(n, 1, -12) for n in xrange(1, 25)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Cf. A001045 and A015441.
Sequence in context: A147145 A151776 A116524 this_sequence A122003 A123827 A105796
Adjacent sequences: A053401 A053402 A053403 this_sequence A053405 A053406 A053407
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KEYWORD
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easy,nonn
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AUTHOR
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Barry E. Williams, Jan 07 2000
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Feb 02 2000
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