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 A301451 Numbers congruent to {1, 7} mod 9. 4
 1, 7, 10, 16, 19, 25, 28, 34, 37, 43, 46, 52, 55, 61, 64, 70, 73, 79, 82, 88, 91, 97, 100, 106, 109, 115, 118, 124, 127, 133, 136, 142, 145, 151, 154, 160, 163, 169, 172, 178, 181, 187, 190, 196, 199, 205, 208, 214, 217, 223, 226, 232, 235, 241, 244, 250, 253, 259, 262, 268 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First bisection of A056991, second bisection of A242660. The squares of the terms of A174396 are the squares of this sequence. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). FORMULA O.g.f.: x*(1 + 6*x + 2*x^2)/((1 + x)*(1 - x)^2). E.g.f.: (3 + 8*exp(x) - 11*exp(2*x) + 18*x*exp(2*x))*exp(-x)/4. a(n) = a(n-1) + a(n-2) - a(n-3). a(n) = 2*(2*n - 1) + (2*n - 3*(1 - (-1)^n))/4. Therefore, for n even a(n) = (9*n - 4)/2, otherwise a(n) = (9*n - 7)/2. a(2n+1) = A017173(n). a(2n) = A017245(n-1). - R. J. Mathar, Feb 28 2019 MATHEMATICA Table[2 (2 n - 1) + (2 n - 3 (1 - (-1)^n))/4, {n, 1, 60}] PROG (GAP) a := [1, 7, 10];; for n in [4..60] do a[n] := a[n-1] + a[n-2] - a[n-3]; od; a; (Python) [2*(2*n-1)+(2*n-3*(1-(-1)**n))/4 for n in range(1, 70)] (Sage) [n for n in (1..300) if n % 9 in (1, 7)] (MAGMA) &cat [[9*n+1, 9*n+7]: n in [0..40]]; (PARI) Vec(x*(1 + 6*x + 2*x^2) / ((1 - x)^2*(1 + x)) + O(x^60)) \\ Colin Barker, Mar 22 2018 CROSSREFS Cf. A274406: numbers congruent to {0, 8} mod 9. Cf. A193910: numbers congruent to {2, 6} mod 9. Subsequence of A016777, A026225, A029739, A033627, A047236, A047259, A055047, A055054, A056991, A153053, A187318, A242660. Sequence in context: A083390 A234093 A287567 * A033817 A286873 A218128 Adjacent sequences:  A301448 A301449 A301450 * A301452 A301453 A301454 KEYWORD nonn,easy AUTHOR Bruno Berselli, Mar 21 2018 STATUS approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)