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A060482 New record highs reached in A060030. 25
1, 2, 3, 5, 9, 13, 21, 29, 45, 61, 93, 125, 189, 253, 381, 509, 765, 1021, 1533, 2045, 3069, 4093, 6141, 8189, 12285, 16381, 24573, 32765, 49149, 65533, 98301, 131069, 196605, 262141, 393213, 524285, 786429, 1048573, 1572861, 2097149, 3145725 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,2,-2).

FORMULA

a(n) = a(n-1) + 2^((n-1)/2) = 2*a(n-2) + 3 = a(n-1) + A016116(n-1) = A027383(n-1) - 1 = 2*A027383(n-3) + 1 = 4*A052955(n-4) + 1. a(2n) = 2^(n+1) - 3; a(2n+1) = 3*2^n - 3.

From Colin Barker, Jan 12 2013: (Start)

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) for n > 5.

G.f.: x*(2*x^4-x^2+x+1) / ((x-1)*(2*x^2-1)). (End)

MATHEMATICA

LinearRecurrence[{1, 2, -2}, {1, 2, 3, 5, 9}, 50] (* Harvey P. Dale, Sep 11 2016 *)

PROG

(PARI) { for (n=1, 1000, if (n%2==0, m=n/2; a=2^(m + 1) - 3, m=(n - 1)/2; a=3*2^m - 3); if (n<3, a=n); write("b060482.txt", n, " ", a); ) } \\ Harry J. Smith, Jul 05 2009

CROSSREFS

Cf. A060013, A060030.

The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A029744 = {s(n), n>=1}, the numbers 2^k and 3*2^k, as the parent: A029744 (s(n)); A052955 (s(n)-1), A027383 (s(n)-2), A354788 (s(n)-3), A347789 (s(n)-4), A209721 (s(n)+1), A209722 (s(n)+2), A343177 (s(n)+3), A209723 (s(n)+4); A060482, A136252 (minor differences from A354788 at the start); A354785 (3*s(n)), A354789 (3*s(n)-7). The first differences of A029744 are 1,1,1,2,2,4,4,8,8,... which essentially matches eight sequences: A016116, A060546, A117575, A131572, A152166, A158780, A163403, A320770. The bisections of A029744 are A000079 and A007283. - N. J. A. Sloane, Jul 14 2022

Sequence in context: A049715 A076095 A085913 * A018138 A336631 A228129

Adjacent sequences:  A060479 A060480 A060481 * A060483 A060484 A060485

KEYWORD

nonn,easy

AUTHOR

Henry Bottomley, Mar 19 2001

STATUS

approved

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Last modified September 26 01:31 EDT 2022. Contains 356986 sequences. (Running on oeis4.)