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

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-2).

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

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 *)

Crossrefs

Cf. A000051, A060000.

Sequence in context: A065956 A328078 A178738 * A092424 A167510 A351359

Adjacent sequences: A060010 A060011 A060012 * A060014 A060015 A060016

Keyword

nonn,easy

Author

Robert G. Wilson v, Mar 15 2001

Extensions

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

Status

approved