A060013 New record highs reached in A060000.

1, 2, 3, 5, 9, 15, 27, 51, 99, 195, 387, 771, 1539, 3075, 6147, 12291, 24579, 49155, 98307, 196611, 393219, 786435, 1572867, 3145731, 6291459, 12582915, 25165827, 50331651, 100663299, 201326595, 402653187, 805306371, 1610612739, 3221225475, 6442450947, 12884901891

Offset: 1

Author

Robert G. Wilson v, Mar 15 2001

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A000051, A060000.

Programs

Mathematica

h = f = {1, 2}; a = 1; b = 2; Do[ g = Sort[ h ]; If[ g[ [ -1 ] ] + 1 == n, c = a + b, k = 1; While[ g[ [ k ] ] == k, k++ ]; c = k ]; a = b; b = c; h = Append[ h, c ]; If[ c > g[ [ -1 ] ], f = Append[ f, c ] ], { n, 3, 10^4 } ]; f
LinearRecurrence[{3,-2},{1,2,3,5,9,15},40] (* Harvey P. Dale, Dec 12 2018 *)

Formula

For n>4: a(n) = 2*a(n-1)-3. For n>3: a(n) = 3*2^(n-3)+3 = 3*A000051(n-3) = A007283(n-3)+3.

a(n+1) = A060000(a(n)+1), a(1) = 1. - Reinhard Zumkeller, Mar 04 2008

G.f.: -x*(x^2-x+1)*(2*x^3+2*x^2-1) / ((x-1)*(2*x-1)). - Colin Barker, Jan 12 2013

E.g.f.: (144*exp(x) + 9*exp(2*x) - 153 - 114*x - 42*x^2 - 12*x^3 - 2*x^4)/48. - Stefano Spezia, Jul 25 2024

Extensions

Formulae and more terms from Henry Bottomley and Larry Reeves (larryr(AT)acm.org), Mar 19 2001