A087160 -id:A087160 - cp's OEIS frontend

A087159 Satisfies a(1)=1, a(A087160(n+1)) = a(n)+1, with a(m)=2 for all m not found in A087160, where A087160(n+2)=A087160(n+1)+a(n)+1.

1, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 5, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 4, 2, 2, 2, 3, 2, 2, 3, 2, 2, 6, 2, 2, 2, 2, 2, 3, 2

Offset: 1

Paul D. Hanna, Aug 22 2003

nonn

Records form A087161: a(A087161(n))=n and satisfy recurrence: A087161(n+3) = 5*A087161(n+2) - 6*A087161(n+1) + 2*A087161(n).

			Initialize all terms to 2. Set a(1)=1, go one term forward,
set a(2)=a(1)+1=2, go 2 terms forward,
set a(4)=a(2)+1=3, go 3 terms forward,
set a(7)=a(3)+1=3, go 3 terms forward,
set a(10)=a(4)+1=4, go 4 terms forward,
set a(14)=a(5)+1=3, etc.
The indices 1,2,4,7,10,14,... form A087160.

Cf. A087160, A087161.

A087161 Records in A087159, i.e., A087159(a(n)) = n, and satisfies the recurrence a(n+3) = 5a(n+2) - 6 a(n+1) + 2*a(n) with a(1) = 1, a(2) = 2, and a(3) = 4.

Original entry on oeis.org

1, 2, 4, 10, 30, 98, 330, 1122, 3826, 13058, 44578, 152194, 519618, 1774082, 6057090, 20680194, 70606594, 241065986, 823050754, 2810071042, 9594182658, 32756588546, 111837988866, 381838778370, 1303679135746, 4451038986242

Offset: 1

Paul D. Hanna, Aug 22 2003

nonn

Binomial transform of A001333 (which, with an extra leading 1, is the expansion of (1 - x - 2*x^2)/(1 - 2*x - x^2)). - Paul Barry, Aug 26 2003

Partial sums of the binomial transform of Pell(n-1). - Paul Barry, Apr 24 2004

Index entries for linear recurrences with constant coefficients, signature (5,-6,2).

Cf. A000129, A007070, A087159, A087160, A100631.

CoefficientList[Series[(1-3x)/(1-5x+6x^2-2x^3),{x,0,30}],x] (* or *) LinearRecurrence[{5,-6,2},{1,2,4},30] (* Harvey P. Dale, Oct 12 2015 *)

G.f.: x*(1 - 3*x)/(1 - 5*x + 6*x^2 - 2*x^3).
a(n) = 2 + 2*A007070(n-3) for n > 2.
a(n) = ((2 - sqrt(2))^(n)/(1 - sqrt(2)) + (2 + sqrt(2))^(n)/(1 + sqrt(2)))/2 + 2 (offset 0) - Paul Barry, Aug 26 2003
a(n+1) - a(n) = A006012(n-1) for n >= 2. - Philippe Deléham, Feb 01 2012
a(1) = 1, a(2) = 2, a(3) = 4, a(n) = 5*a(n-1) - 6*a(n-2) + 2*a(n-3) for n >= 4. - Harvey P. Dale, Oct 12 2015
a(n+1) = Sum_{k=0..n} A100631(n,k) for n >= 0. - Petros Hadjicostas, Feb 09 2021

More terms from Paul Barry, Apr 24 2004

cp's OEIS Frontend

A087159 Satisfies a(1)=1, a(A087160(n+1)) = a(n)+1, with a(m)=2 for all m not found in A087160, where A087160(n+2)=A087160(n+1)+a(n)+1.

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A087161 Records in A087159, i.e., A087159(a(n)) = n, and satisfies the recurrence a(n+3) = 5a(n+2) - 6 a(n+1) + 2*a(n) with a(1) = 1, a(2) = 2, and a(3) = 4.

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cp's OEIS Frontend

A087159 Satisfies a(1)=1, a(A087160(n+1)) = a(n)+1, with a(m)=2 for all m not found in A087160, where A087160(n+2)=A087160(n+1)+a(n)+1.

Views

Author

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Comments

Examples

Crossrefs

A087161 Records in A087159, i.e., A087159(a(n)) = n, and satisfies the recurrence a(n+3) = 5*a(n+2) - 6* a(n+1) + 2*a(n) with a(1) = 1, a(2) = 2, and a(3) = 4.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A087161 Records in A087159, i.e., A087159(a(n)) = n, and satisfies the recurrence a(n+3) = 5a(n+2) - 6 a(n+1) + 2*a(n) with a(1) = 1, a(2) = 2, and a(3) = 4.