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

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Last modified May 29 01:41 EDT 2022. Contains 354122 sequences. (Running on oeis4.)