Penny Spiral Sequence

Origin of EIS sequences A047931 & A047932

Put a second one next to the first.
The two pennies make 1 contact.

Put a third penny on the table, maximizing the number of new contacts.
There are 2 new contacts.

Put a fourth penny on the table, maximizing the number of new contacts.
There are 2 new contacts.

Etc.

The pattern of adding pennies follows a spiral.
The pennies are arranged on the edges and vertices of hexagons.
The initial hexagon (h=0) is degenerated to a point.
The next hexagon (h=1) has six pennies, all on vertices.
For h=2 there are 12 pennies, 1/2 of them on vertices, 1/2 on edges.
For h=3 there are 18 pennies, 1/3 of them on vertices, 2/3 on edges.
Etc.

The integer sequence of new contacts is:

h=0: 0
h=1: 1  2  2  2  2  3
h=2: 2 2  3 2  3 2  3 2  3 2  3 3
h=3: 2 3 2  3 3 2  3 3 2  3 3 2  3 3 2  3 3 3
h=4: 2 3 3 2  3 3 3 2  3 3 3 2  3 3 3 2  3 3 3 2  3 3 3 3
h=5: 2 3 3 3 2  3 3 3 3 2  3 3 3 3 2  3 3 3 3 2  3 3 3 3 2  3 3 3 3 3
...
h=n: 2 3{n-2} 2  3{n-1} 2  3{n-1} 2  3{n-1} 2  3{n-1} 2  3{n}

a{b} symbolizes b repetitions of a

The cumulative sum sequence is:

0 1 3 5 7 9 12 14 16 19 21 24 26 29 31 34 36 39 42 44 47 49 52 55 57
60 63 65 68 71 73 76 79 81 84 87 90 92 95 98 100 103 106 109 111 114
117 120 122 125 128 131 133 136 139 142 144 147 150 153 156 158 161
164 167 169 172 175 178 181 183 186 189 192 195 197 200 203 206 209
211 214 217 220 223 225 228 231 234 237 240