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 A076293 Numbers k where the root mean square (RMS) of k and 7 is an integer, i.e., sqrt((k^2 + 7^2)/2) is an integer. 4
 1, 7, 17, 23, 49, 103, 137, 287, 601, 799, 1673, 3503, 4657, 9751, 20417, 27143, 56833, 118999, 158201, 331247, 693577, 922063, 1930649, 4042463, 5374177, 11252647, 23561201, 31322999, 65585233, 137324743, 182563817, 382258751, 800387257, 1064059903 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..2000 Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Classes of Gap Balancing Numbers, arXiv:1810.07895 [math.NT], 2018. Jeremiah Bartz, Bruce Dearden, and Joel Iiams, Counting families of generalized balancing numbers, The Australasian Journal of Combinatorics (2020) Vol. 77, Part 3, 318-325. Index entries for linear recurrences with constant coefficients, signature (0,0,6,0,0,-1). FORMULA a(n) = 6a(n-3) - a(n-6) = sqrt(2*A076294(n)^2 - 49) = A076295(n) + A076296(n). a(3n+1) = 7*A002315(n). G.f.: (x+1)*(x^2+3*x+1)^2 / (x^6-6*x^3+1). - Colin Barker, Sep 14 2014 EXAMPLE 17 is in the sequence since sqrt((17^2 + 7^2)/2) = 13 is an integer. MATHEMATICA Column[LinearRecurrence[{0, 0, 6, 0, 0, -1}, {1, 7, 17, 23, 49, 103}, 35] ] (* Vincenzo Librandi, Jul 30 2017 *) PROG (PARI) Vec((x+1)*(x^2+3*x+1)^2/(x^6-6*x^3+1) + O(x^100)) \\ Colin Barker, Sep 14 2014 CROSSREFS Cf. A002315, A076294, A076295, A076296. Sequence in context: A265810 A026349 A057183 * A227276 A300298 A273745 Adjacent sequences:  A076290 A076291 A076292 * A076294 A076295 A076296 KEYWORD nonn,easy AUTHOR Henry Bottomley, Oct 05 2002 EXTENSIONS More terms from Colin Barker, Sep 14 2014 STATUS approved

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Last modified August 1 00:13 EDT 2021. Contains 346377 sequences. (Running on oeis4.)