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Search: id:A048573
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| A048573 |
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a(n) = a(n-1) + 2a(n-2), a(0)=2, a(1)=3. |
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+0
4
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| 2, 3, 7, 13, 27, 53, 107, 213, 427, 853, 1707, 3413, 6827, 13653, 27307, 54613, 109227, 218453, 436907, 873813, 1747627, 3495253, 6990507, 13981013, 27962027, 55924053, 111848107, 223696213, 447392427, 894784853, 1789569707
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Number of positive integers requiring exactly n signed bits in the modified non-adjacent form representation. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 02 2003
The n-th entry (n>1) of the sequence is equal to the 1,1-entry of the n-th power of the unnormalized 4 by 4 Haar matrix: [1 1 1 0 / 1 1 -1 0 / 1 1 0 1 / 1 1 0 -1]. - Simone Severini (ss54(AT)york.ac.uk), Oct 27 2004
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LINKS
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W. Bosma, Signed bits and fast exponentiation
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FORMULA
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G.f.: (2+x)/(1-x-2x^2).
a(n) = (5*2^n+(-1)^n)/3
a(n)=2*A001045(n+1)+A001045(n) (note that 2 is the limit of A001045(n+1)/A001045(n)). [From Paul Barry (pbarry(AT)wit.ie), Sep 14 2009]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (5*2^n+(-1)^n)/3)
(PARI) a(n)=if(n<0, 0, if(n<2, n+2, a(n-1)+2*a(n-2)))
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CROSSREFS
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a(n) = 2^(n+1)-A001045(n).
a(n) = A084170(n)+1 = |A083581(n)-3| = A081254(n+1)-A081254(n) = A084214(n+2)/2.
Sequence in context: A128695 A024504 A088172 this_sequence A006946 A074129 A055003
Adjacent sequences: A048570 A048571 A048572 this_sequence A048574 A048575 A048576
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KEYWORD
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nonn
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AUTHOR
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Michael Somos
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