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A156140
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Accumulation of Stern's diatomic series: a(0)=-1, a(1)=0, a(n+1)-(2e(n)+1).a(n)+a(n-1)=0 (n>=1); e(n) is exponent highest power of 2 dividing n
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1
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-1, 0, 1, 3, 2, 7, 5, 8, 3, 13, 10, 17, 7, 18, 11, 15, 4, 21, 17, 30, 13, 35, 22, 31, 9, 32, 23, 37, 14, 33, 19, 24, 5, 31, 26, 47, 21, 58, 37, 53, 16, 59, 43, 70, 27, 65, 38, 49, 11, 50, 39, 67, 28, 73, 45, 62, 17, 57, 40, 63, 23, 52, 29, 35, 6, 43, 37, 68, 31, 87, 56, 81, 25, 94, 69
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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FORMULA
| Let b(n) = a002487(n), diatomic serie of Stern
a(n+1).b(n) - a(n).b(n+1) = 1 for n >= 0
a(2n+1) = a(n) + a(n+1) + b(n) + b(n+1) for n >= 0
a(2n) = a(n) + b(n) for n >= 0
a(2^n + k) = -n.a(k) + (n^2 + n + 1).b(k) for 0 <= k <= 2^n
b(2^n + k) = -a(k) + (n + 1).b(k) for 0 <= k <= 2^n
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MAPLE
| A007814 := proc(n) local ifs, p; ifs := ifactors(n)[2] ; for p in ifs do if op(1, p) = 2 then RETURN(op(2, p) ) ; fi; od: RETURN(0) ; end: A156140 := proc(n) option remember ; if n <= 1 then n-1 ; else (2*A007814(n-1)+1)*procname(n-1)-procname(n-2) ; fi; end: seq(A156140(n), n=0..80) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2009]
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CROSSREFS
| Cf. A002487, A007814
Sequence in context: A126314 A200714 A086702 * A069888 A073281 A130922
Adjacent sequences: A156137 A156138 A156139 * A156141 A156142 A156143
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KEYWORD
| uned,sign
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AUTHOR
| Arie Werksma (Werksma(AT)Tiscali.nl), Feb 04 2009
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 14 2009
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