|
%I #17 Nov 03 2021 06:08:24
%S 3,10,15,20,27,32,39,44,51,56,61,68,73,80,85,90,97,102,109,114,119,
%T 126,131,138,143,150,155,160,167,172,179,184,189,196,201,208,213,220,
%U 225,230,237,242,249,254,259,266,271,278,283,290,295,300,307,312,319
%N The sequence C(n) defined in the comments (A and B smallest missing numbers, offset 0).
%C Define a triple of sequences A,B,C by A[0]=1, B[0]=2, C[0]=3; for n>=1, A[n] = smallest missing number from the terms of A,B,C defined so far; B[n] = = smallest missing number from the terms of A,B,C defined so far; C[n] = n+A[n]+B[n].
%C Then A = A086377, B = A080652, C = the present sequence.
%C Inspired by the triples [A003144, A003145, A004146] and [A298468, A298469, A047218].
%F Conjectures from _Colin Barker_, Nov 08 2019: (Start)
%F G.f.: (3 + 7*x + 5*x^2 + 5*x^3 + 7*x^4 + 5*x^5 + 7*x^6 + 5*x^7 + 7*x^8 + 5*x^9 + 5*x^10 + 7*x^11 + 2*x^12 - 2*x^20 + 2*x^21) / (1 - x - x^12 + x^13).
%F a(n) = a(n-1) + a(n-12) - a(n-13) for n>21.
%F (End)
%F Conjecture: a(n) ~ 35*n/6. - _Stefano Spezia_, Nov 02 2021
%e The initial terms are:
%e n: 0, 1, 2, 3, 4, 5, 6, 7, 8. 9. 10. ...
%e a: 1, 4, 6, 8, 11, 13, 16, 18, 21, 23,25, ...
%e b: 2, 5, 7, 9, 12, 14, 17, 19, 22, 24,26, ...
%e c: 3, 10, 15, 20, 27, 32, 39, 44, 51, 56, 61, 68, 73, ...
%Y Cf. A086377, A080652; A003144, A003145, A003146; A298468, A298469, A047218.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Nov 07 2019
|
