A220154 -id:A220154 - cp's OEIS frontend

A230370 Voids left after packing 3 curves coins patterns (3c3s type) into fountain of coins base n.

0, 0, 3, 6, 13, 19, 39, 54, 66, 85, 100, 123, 141, 168, 189, 220, 244, 279, 306, 345, 375, 418, 451, 498, 534, 585, 624, 679, 721, 780, 825, 888, 936, 1003, 1054, 1125, 1179, 1254, 1311, 1390, 1450, 1533, 1596, 1683

Offset: 1

Kival Ngaokrajang, Oct 17 2013

nonn

Refer to arrangement same as A005169: "A fountain is formed by starting with a row of coins, then stacking additional coins on top so that each new coin touches two in the previous row". The 3 curves coins patterns consist of a part of each coin circumference and forms a continuous area. There are total 4 distinct patterns. For selected pattern, I would like to call "3c3s" type as it cover 3 coins and symmetry. When packing 3c3s into fountain of coins base n, the total number of 3c3s is A008805, the coins left is A008795 and voids left is a(n). See illustration in links.

Kival Ngaokrajang, Illustration of initial terms (V)

A001399, A230267, A230276 (5-curves coins patterns); A074148, A229093, A220154 (4-curves coins patterns); A008795 (3-curves coins patterns).

G.f.: x^3*(11*x^8 - 5*x^7 - 21*x^6 + 6*x^5 + 9*x^4 + x^2 + 3*x + 3)/((1-x)*(1-x^2)^2) (conjectured). Ralf Stephan, Oct 19 2013

cp's OEIS Frontend

A230370 Voids left after packing 3 curves coins patterns (3c3s type) into fountain of coins base n.

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