Partitioned Sequence / Identity - sql-server

Question

Given a table like this
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
CREATE TABLE [dbo].[_bh_test](
[Id] [bigint] IDENTITY(1,1) NOT NULL,
[Agency] [int] NOT NULL,
[Year] [int] NULL,
[Num] [int] NOT NULL
) ON [PRIMARY]
GO
SET IDENTITY_INSERT [dbo].[_bh_test] ON
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (1, 1, 2015, 1)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (2, 1, 2015, 2)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (3, 1, 2016, 1)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (4, 2, 2015, 1)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (5, 2, 2015, 2)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (6, 2, 2016, 1)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (7, 2, 2016, 2)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (8, 3, 2015, 1)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (9, 3, 2015, 2)
GO
INSERT [dbo].[_bh_test] ([Id], [Agency], [Year], [Num]) VALUES (10, 3, 2016, 2)
GO
SET IDENTITY_INSERT [dbo].[_bh_test] OFF
GO
/****** Object: Index [UIX_Agency_Year_Num] Script Date: 4/17/2017 10:42:15 PM ******/
CREATE UNIQUE NONCLUSTERED INDEX [UIX_Agency_Year_Num] ON [dbo].[_bh_test]
(
[Agency] ASC,
[Year] ASC,
[Num] ASC
)WITH (PAD_INDEX = OFF, STATISTICS_NORECOMPUTE = OFF, SORT_IN_TEMPDB = OFF, IGNORE_DUP_KEY = OFF, DROP_EXISTING = OFF, ONLINE = OFF, ALLOW_ROW_LOCKS = ON, ALLOW_PAGE_LOCKS = ON) ON [PRIMARY]
GO
I want the Num column to always have a value that is unique across that particular Agency when inserting. Additionally, I want it to be a number that has never been used before.
So for example if I am inserting a value with agency 3, then a good candidate for Num would be 3.
It would seem I could use a default/binding to a function that would take the MAX(Num) + 1 with a group by for Agency. However, I wasnt able to send in the Agency to the function. But futhermore if the MAX(Num) was 2 and I inserted in 3...Then deleted 3, and inserted again it would reuse a Num of 3, which is wrong because I only want it to use a Num that has never been used before.
It sounds like an ideal solution for me would be a sequence that keeps track of a counter. Although it seems I cant used the PARTITION BY in the OVER in a SEQUENCE. Also the Num may be set manually so If the sequence was +1, and two values were inserted using the default seq. so now counter is at 2...it may be that 3 is manually inserted, and then next insert by default would be 3. I would have to make sure to update the sequence on INSERT
I am not sure the best approach. I think using an INSERT TRIGGER is an option but I am not sure how to get around the whole problem if the MAX() is deleted and an INSERT is done.