# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a186029 Showing 1-1 of 1 %I A186029 #58 Sep 08 2022 08:45:55 %S A186029 0,5,17,36,62,95,135,182,236,297,365,440,522,611,707,810,920,1037, %T A186029 1161,1292,1430,1575,1727,1886,2052,2225,2405,2592,2786,2987,3195, %U A186029 3410,3632,3861,4097,4340,4590,4847,5111,5382,5660,5945,6237,6536,6842,7155,7475 %N A186029 a(n) = n*(7*n+3)/2. %C A186029 This sequence is related to A050409 by A050409(n) = n*a(n) - Sum_{i=0..n-1} a(i). %H A186029 Vincenzo Librandi, Table of n, a(n) for n = 0..1000 %H A186029 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). %F A186029 G.f.: x*(5+2*x)/(1-x)^3. %F A186029 a(n) - a(-n) = A008585(n). %F A186029 a(n) + a(-n) = A033582(n). %F A186029 n*a(n+1) - (n+1)*a(n) = A024966(n). - _Bruno Berselli_, May 30 2012 %F A186029 n*a(n+2) - (n+2)*a(n) = A067727(n) for n>0. - _Bruno Berselli_, May 30 2012 %F A186029 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2, a(0)=0, a(1)=5, a(2)=17. - _Philippe Deléham_, Mar 26 2013 %F A186029 a(n) = A174738(7*n+4). - _Philippe Deléham_, Mar 26 2013 %F A186029 E.g.f.: (1/2)*(7*x^2 + 10*x)*exp(x). - _G. C. Greubel_, Jul 17 2017 %e A186029 From _Ilya Gutkovskiy_, Mar 31 2016: (Start) %e A186029 . o o o o o o o o o o o o %e A186029 . o o %e A186029 . o o o o o o o o o o o o o o o o o o o o o o o o %e A186029 . o o o o o o o o o o o o %e A186029 . o o o o o o o o o o o o o o o o o o o o %e A186029 . o o o o o o o o o o o o o o o o o o o o o o o o %e A186029 . o o o o o o %e A186029 . o o o o o o o o o o o o o o o o o o o o %e A186029 . %e A186029 . n=1 n=2 n=3 n=4 %e A186029 (End) %t A186029 Table[(n - 1) (7 n - 4)/2, {n, 100}] (* _Vladimir Joseph Stephan Orlovsky_, Jul 06 2011 *) %t A186029 LinearRecurrence[{3,-3,1},{0,5,17},50] (* _Harvey P. Dale_, Sep 07 2022 *) %o A186029 (Magma) [n*(7*n+3)/2: n in [0..44]]; %o A186029 (PARI) a(n)=n*(7*n+3)/2 \\ _Charles R Greathouse IV_, Sep 24 2015 %Y A186029 Cf. numbers of the form n*(d*n+10-d)/2 indexed in A140090. %Y A186029 Cf. A017041 (first differences). %Y A186029 Cf. A001106, A022264, A022265, A024966, A050409, A067727, A174738, A179986, A218471. %K A186029 nonn,easy %O A186029 0,2 %A A186029 _Bruno Berselli_, Feb 11 2011 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE