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A009694
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a(n) = Product_{i=0..7} floor((n+i)/8).
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10
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0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561, 8748, 11664, 15552, 20736, 27648, 36864, 49152, 65536, 81920, 102400, 128000, 160000, 200000, 250000, 312500
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OFFSET
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0,10
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COMMENTS
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For n >= 8, a(n) is the maximal product of eight positive integers with sum n. - Wesley Ivan Hurt, Jul 08 2022
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (2, -1, 0, 0, 0, 0, 0, 7, -14, 7, 0, 0, 0, 0, 0, -21, 42, -21, 0, 0, 0, 0, 0, 35, -70, 35, 0, 0, 0, 0, 0, -35, 70, -35, 0, 0, 0, 0, 0, 21, -42, 21, 0, 0, 0, 0, 0, -7, 14, -7, 0, 0, 0, 0, 0, 1, -2, 1).
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FORMULA
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Sum_{n>=8} 1/a(n) = 1 + zeta(8). - Amiram Eldar, Jan 10 2023
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MATHEMATICA
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Table[Product[Floor[(n+i)/8], {i, 0, 7}], {n, 0, 40}] (* Harvey P. Dale, Nov 13 2013 *)
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PROG
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(PARI) a(n) = prod(i=0, 7, (n+i)\8); \\ Michel Marcus, Jul 14 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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