A131874 - OEIS

%I #36 Mar 04 2022 01:26:57

%S 1,12,30,55,87,126,172,225,285,352,426,507,595,690,792,901,1017,1140,

%T 1270,1407,1551,1702,1860,2025,2197,2376,2562,2755,2955,3162,3376,

%U 3597,3825,4060,4302,4551,4807,5070,5340,5617,5901,6192,6490,6795,7107,7426

%N a(n) = (7*n^2 + 15*n + 2) / 2.

%C Row sums of triangle A131873.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F Binomial transform of (1, 11, 7, 0, 0, 0, ...).

%F a(n) = a(n-1) + 7*n + 4, (with a(0)=1). - _Vincenzo Librandi_, Nov 23 2010

%F a(n) = (2 + 15*n + 7*n^2)/2;

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3);

%F G.f.: (1 + 9*x - 3*x^2)/ (1-x)^3. - _Colin Barker_, Sep 13 2012

%e a(2) = 30 = sum of row 2 terms of triangle A131873: (15 + 8 + 7).

%e a(2) = 30 = (1, 2, 1) dot (1, 11, 7) = (1 + 22 + 7).

%p A131874:=n->(2+15*n+7*n^2)/2; seq(A131874(n), n=0..100); # _Wesley Ivan Hurt_, Mar 26 2014

%o (PARI) a(n)=(7*n^2+15*n+2)/2 \\ _Charles R Greathouse IV_, Jun 16 2017

%Y Cf. A131873.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Jul 22 2007

%E More terms from _Vladimir Joseph Stephan Orlovsky_, Dec 04 2008