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A101622
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A Horadam-Jacobsthal sequence.
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5
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0, 1, 6, 13, 30, 61, 126, 253, 510, 1021, 2046, 4093, 8190, 16381, 32766, 65533, 131070, 262141, 524286, 1048573, 2097150, 4194301, 8388606, 16777213, 33554430, 67108861, 134217726, 268435453, 536870910, 1073741821, 2147483646
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Companion sequence to A084639.
a(n)=a(n-1)+2a(n-2)+5; a(n)=2a(n-1)+a(n-2)-2a(n-3); a(n)=A000079(n+1)-A010693(n). Note a(n+1)=A141722(n)+5=A141722(n)+A010716(n). a(2n+1)-a(2n)=1,7,31,=A083420. a(2n+1)-2a(2n)=1. a(2n)=A002446=6*A002450, a(2n+1)=A141725. [From Paul Curtz, Jan 01 2009]
This is the sequence A(0,1;1,2;5) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [From Wolfdieter Lang, Oct 18 2010]
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REFERENCES
| A. F. Horadam, Jacobsthal Representation Numbers, Fib. Quart. 34, 40-54, 1996.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
W. Lang, Notes on certain inhomogeneous three term recurrences. [From Wolfdieter Lang, Oct 18 2010]
Index to sequences with linear recurrences with constant coefficients, signature (2,1,-2).
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FORMULA
| a(n) = (2^(n+2)+(-1)^n-5)/2.
G.f.: x*(1+4*x)/((1-x)*(1+x)*(1-2*x)).
a(n) = (A014551(n+2)-5)/2.
(1, 6, 13, 30, 61,...) are the row sums of A131953. - Gary W. Adamson, Jul 31 2007
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PROG
| (MAGMA) [(2^(n+2)+(-1)^n-5)/2: n in [0..35]]; // Vincenzo Librandi, Aug 12 2011
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CROSSREFS
| Cf. A131953.
Sequence in context: A086652 A159694 A145976 * A192304 A147330 A042607
Adjacent sequences: A101619 A101620 A101621 * A101623 A101624 A101625
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Dec 10 2004
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