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A286314
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Number of representations of 10^n as sum of 6 triangular numbers.
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2
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6, 231, 20400, 2003001, 200045352, 20000567352, 1959085094400, 200000030000001, 20118337236261000, 1999999999505541852, 200000000030000000001, 19994255180823548693100, 1959183673472326530612252, 200000000000105810631542400, 20118343160415860069040000000
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OFFSET
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0,1
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COMMENTS
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a(n) is nearly 2*10^(2*n) because a(n) is almost (4*10^n+3)^2 / 8.
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..17
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FORMULA
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a(n) = A008440(10^n).
a(n) = 1/8 * (Sum_{d|4*10^n+3, d == 3 mod 4} d^2 - Sum_{d|4*10^n+3, d == 1 mod 4} d^2).
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EXAMPLE
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a(0) = 1/8 * (Sum_{d|7, d == 3 mod 4} d^2 - Sum_{d|7, d == 1 mod 4} d^2) = 1/8 * (7^2 - 1^2) = 6.
a(1) = 1/8 * (Sum_{d|43, d == 3 mod 4} d^2 - Sum_{d|43, d == 1 mod 4} d^2) = 1/8 * (43^2 - 1^2) = 231.
a(2) = 1/8 * (Sum_{d|403, d == 3 mod 4} d^2 - Sum_{d|403, d == 1 mod 4} d^2) = 1/8 * (403^2 + 31^2 - 13^2 - 1^2) = 20400.
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CROSSREFS
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Cf. A008440, A286315.
Sequence in context: A309009 A117064 A112001 * A099124 A172862 A099129
Adjacent sequences: A286311 A286312 A286313 * A286315 A286316 A286317
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KEYWORD
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nonn
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AUTHOR
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Seiichi Manyama, May 06 2017
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EXTENSIONS
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More terms from Seiichi Manyama, May 07 2017
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STATUS
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approved
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