# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a301451 Showing 1-1 of 1 %I A301451 #28 Sep 08 2022 08:46:20 %S A301451 1,7,10,16,19,25,28,34,37,43,46,52,55,61,64,70,73,79,82,88,91,97,100, %T A301451 106,109,115,118,124,127,133,136,142,145,151,154,160,163,169,172,178, %U A301451 181,187,190,196,199,205,208,214,217,223,226,232,235,241,244,250,253,259,262,268 %N A301451 Numbers congruent to {1, 7} mod 9. %C A301451 First bisection of A056991, second bisection of A242660. %C A301451 The squares of the terms of A174396 are the squares of this sequence. %H A301451 Colin Barker, Table of n, a(n) for n = 1..1000 %H A301451 Index entries for linear recurrences with constant coefficients, signature (1,1,-1). %F A301451 O.g.f.: x*(1 + 6*x + 2*x^2)/((1 + x)*(1 - x)^2). %F A301451 E.g.f.: (3 + 8*exp(x) - 11*exp(2*x) + 18*x*exp(2*x))*exp(-x)/4. %F A301451 a(n) = a(n-1) + a(n-2) - a(n-3). %F A301451 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. %F A301451 a(2n+1) = A017173(n). a(2n) = A017245(n-1). - _R. J. Mathar_, Feb 28 2019 %t A301451 Table[2 (2 n - 1) + (2 n - 3 (1 - (-1)^n))/4, {n, 1, 60}] %t A301451 {#+1,#+7}&/@(9*Range[0,30])//Flatten (* or *) LinearRecurrence[{1,1,-1},{1,7,10},60] (* _Harvey P. Dale_, Nov 08 2020 *) %o A301451 (GAP) a := [1,7,10];; for n in [4..60] do a[n] := a[n-1] + a[n-2] - a[n-3]; od; a; %o A301451 (Python) [2*(2*n-1)+(2*n-3*(1-(-1)**n))/4 for n in range(1,70)] %o A301451 (Sage) [n for n in (1..300) if n % 9 in (1,7)] %o A301451 (Magma) &cat [[9*n+1, 9*n+7]: n in [0..40]]; %o A301451 (PARI) Vec(x*(1 + 6*x + 2*x^2) / ((1 - x)^2*(1 + x)) + O(x^60)) \\ _Colin Barker_, Mar 22 2018 %Y A301451 Cf. A274406: numbers congruent to {0, 8} mod 9. %Y A301451 Cf. A193910: numbers congruent to {2, 6} mod 9. %Y A301451 Subsequence of A016777, A026225, A029739, A033627, A047236, A047259, A055047, A055054, A056991, A153053, A187318, A242660. %K A301451 nonn,easy %O A301451 1,2 %A A301451 _Bruno Berselli_, Mar 21 2018 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE