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A009641
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a(n) = Product_{i=0..6} floor((n+i)/7).
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12
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0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 8, 16, 32, 64, 128, 192, 288, 432, 648, 972, 1458, 2187, 2916, 3888, 5184, 6912, 9216, 12288, 16384, 20480, 25600, 32000, 40000, 50000, 62500, 78125, 93750, 112500, 135000, 162000, 194400, 233280, 279936, 326592, 381024
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OFFSET
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0,9
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COMMENTS
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For n >= 7, a(n) is the maximal product of seven positive integers with sum n. - Wesley Ivan Hurt, Jun 29 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, 6, -12, 6, 0, 0, 0, 0, -15, 30, -15, 0, 0, 0, 0, 20, -40, 20, 0, 0, 0, 0, -15, 30, -15, 0, 0, 0, 0, 6, -12, 6, 0, 0, 0, 0, -1, 2, -1).
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FORMULA
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a(n) = 2*a(n-1) - a(n-2) + 6*a(n-7) - 12*a(n-8) + 6*a(n-9) - 15*a(n-14) + 30*a(n-15) - 15*a(n-16) + 20*a(n-21) - 40*a(n-22) + 20*a(n-23) - 15*a(n-28) + 30*a(n-29) - 15*a(n-30) + 6*a(n-35) - 12*a(n-36) + 6*a(n-37) - a(n-42) + 2*a(n-43) - a(n-44). - Wesley Ivan Hurt, Jun 29 2022
Sum_{n>=7} 1/a(n) = 1 + zeta(7). - Amiram Eldar, Jan 10 2023
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PROG
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(PARI) a(n) = prod(k=0, 6, (n+k)\7); \\ Georg Fischer, Nov 07 2019
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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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EXTENSIONS
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STATUS
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approved
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