A158842 - OEIS

%I #37 Feb 14 2023 19:56:07

%S 1,1,4,13,31,61,106,169,253,361,496,661,859,1093,1366,1681,2041,2449,

%T 2908,3421,3991,4621,5314,6073,6901,7801,8776,9829,10963,12181,13486,

%U 14881,16369,17953,19636,21421,23311,25309,27418,29641,31981,34441,37024,39733,42571,45541,48646

%N a(n) = 1 + n*(n+1)*(n-1)/2.

%C Binomial transform of the sequence 1, 0, 3, 3, 0, 0, 0, ... .

%H Vincenzo Librandi, <a href="/A158842/b158842.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%F a(n) = 1+A027480(n-1) for n>=1. - _R. J. Mathar_, Mar 28 2009

%F G.f.: 1-x*(-1-3*x^2+x^3) / (x-1)^4 . - _R. J. Mathar_, Nov 05 2011

%F E.g.f.: exp(x)*(1 + x^3/2 + 3*x^2/2). - _Nikolaos Pantelidis_, Feb 13 2023

%e a(4) = 31 = sum of row 4 terms of triangle A158841: (13 + 9 + 6 + 3).

%p A158842 := proc(n)

%p         1+n*(n+1)*(n-1)/2 ;

%p end proc:

%p seq(A158842(n),n=0..30) ; # _R. J. Mathar_, Nov 05 2011

%t Table[1 + n*(n + 1)*(n - 1)/2, {n, 40}] (* and *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 13, 31}, 40] (* _Vladimir Joseph Stephan Orlovsky_, Feb 21 2012 *)

%o (Magma) [1+ n*(n+1)*(n-1)/2: n in [1..50]]; // _Vincenzo Librandi_, Nov 16 2011

%Y Row sums of A158841.

%K nonn,easy

%O 0,3

%A _Gary W. Adamson_ & _Roger L. Bagula_, Mar 28 2009

%E a(0)=1 prepended by _Andrew Howroyd_, Feb 14 2023