A319702 Filter sequence for sequences that are constant for all even terms >= 2.

1, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 10, 2, 11, 2, 12, 2, 13, 2, 14, 2, 15, 2, 16, 2, 17, 2, 18, 2, 19, 2, 20, 2, 21, 2, 22, 2, 23, 2, 24, 2, 25, 2, 26, 2, 27, 2, 28, 2, 29, 2, 30, 2, 31, 2, 32, 2, 33, 2, 34, 2, 35, 2, 36, 2, 37, 2, 38, 2, 39, 2, 40, 2, 41, 2, 42, 2, 43, 2, 44, 2, 45, 2, 46, 2, 47, 2, 48, 2, 49, 2, 50, 2, 51, 2, 52, 2, 53, 2, 54, 2, 55, 2, 56, 2, 57, 2, 58, 2, 59, 2, 60, 2, 61, 2

Offset: 1

Author

Antti Karttunen, Oct 02 2018

Keywords

• nonn
• easy

Comments

Restricted growth sequence transform of A141310.

For n > 2, a(n-1) is the number of occurrences of n in A319840. - Stefano Spezia, Apr 07 2023

Links

• Antti Karttunen, Table of n, a(n) for n = 1..100000
• Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Crossrefs

Cf. A141310, A319701, A319840.

Programs

PARI

A319702(n) = if(n<=2, n, if(!(n%2), 2, (n+3)/2));

Formula

a(1) = 1, and for n > 1, if n is even, a(n) = 2, otherwise a(n) = (n+3)/2.

From Stefano Spezia, Apr 07 2023: (Start)

O.g.f.: x*(1 + 2*x + x^2 - 2*x^3 - x^4)/((1 - x)^2*(1 + x)^2).

E.g.f.: ((4 + x)*cosh(x) + 3*sinh(x) - 2*(2 + x))/2. (End)