# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a060163 Showing 1-1 of 1 %I A060163 #40 Nov 20 2023 15:23:56 %S A060163 0,2,3,4,6,10,17,28,44,66,95,132,178,234,301,380,472,578,699,836,990, %T A060163 1162,1353,1564,1796,2050,2327,2628,2954,3306,3685,4092,4528,4994, %U A060163 5491,6020,6582,7178,7809,8476,9180,9922,10703,11524,12386,13290,14237 %N A060163 a(n) = (n^3 + 5*n + 18)/6. %C A060163 a(n) = (m^2 - 6*m + 17)*m/6 where m = n+2. - _Frank Ellermann_ %H A060163 Harry J. Smith, Table of n, a(n) for n = -2..1000 %H A060163 Ângela Mestre and José Agapito, Square Matrices Generated by Sequences of Riordan Arrays, J. Int. Seq., Vol. 22 (2019), Article 19.8.4. %H A060163 Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1). %F A060163 a(n) = a(n-1) + A000124(n-1) = A060162(n+3, n) = A004006(n)+3 = A000125(n) + 2. %F A060163 It appears that a(n) = A011826(n+1) + 1. %F A060163 a(n) = n + 2 + binomial(n,3) (with different offset). - _Zerinvary Lajos_, Jul 23 2006 %F A060163 G.f.: (2 - 5*x + 4*x^2)/(x*(1 - x)^4). - _Stefano Spezia_, Nov 19 2023 %p A060163 seq((n^3 + 5*n + 18)/6, n=-2..46); # _Zerinvary Lajos_, Jul 23 2006 %t A060163 a=2;s=3;lst={-3,-1,0,1,s};Do[a+=n;s+=a;AppendTo[lst,s],{n,2,6!,1}];lst+3 (* _Vladimir Joseph Stephan Orlovsky_, May 24 2009 *) %t A060163 Table[(n^3+5n+18)/6,{n,-2,50}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,2,3,4},50] (* _Harvey P. Dale_, Mar 11 2015 *) %o A060163 (PARI) { for (n=-2, 1000, write("b060163.txt", n, " ", (n^3 + 5*n + 18)/6); ) } \\ _Harry J. Smith_, Jul 02 2009 %o A060163 (Magma) [(n^3+5*n+18)/6 : n in [-2..50]]; // _Wesley Ivan Hurt_, Mar 25 2020 %Y A060163 Cf. A000124, A000125, A004006, A011826, A060162. %K A060163 easy,nonn %O A060163 -2,2 %A A060163 _Henry Bottomley_, Mar 13 2001 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE