A131895 - OEIS

%I #30 Oct 23 2024 14:40:05

%S 1,9,22,40,63,91,124,162,205,253,306,364,427,495,568,646,729,817,910,

%T 1008,1111,1219,1332,1450,1573,1701,1834,1972,2115,2263,2416,2574,

%U 2737,2905,3078,3256,3439,3627,3820,4018,4221,4429,4642,4860,5083,5311,5544

%N a(n) = (n + 2)*(5*n + 1)/2.

%C Row sums of triangle A131894.

%C Binomial transform of (1, 8, 5, 0, 0, 0, ...).

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

%F a(n) = a(n-1) + 5*n + 3 (with a(0)=1). - _Vincenzo Librandi_, Nov 23 2010

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=1, a(1)=9, a(2)=22. - _Harvey P. Dale_, Sep 11 2015

%F From _Elmo R. Oliveira_, Oct 22 2024: (Start)

%F G.f.: (1 + 6*x - 2*x^2)/(1 - x)^3.

%F E.g.f.: (1 + 8*x + 5*x^2/2)*exp(x). (End)

%e a(2) = 22 = sum of row 2 terms of triangle A131894: (11 + 6 + 5).

%e a(2) = 22 = (1, 2, 1) dot (1, 8, 5) = (1 + 16 + 5).

%p A131895:=n->(n+2)*(5*n+1)/2; seq(A131895(n), n=0..50); # _Wesley Ivan Hurt_, Mar 26 2014

%t LinearRecurrence[{3,-3,1},{1,9,22},50] (* _Harvey P. Dale_, Sep 11 2015 *)

%o (PARI) a(n)=(n+2)*(5*n+1)/2 \\ _Charles R Greathouse IV_, Jun 17 2017

%Y Cf. A131894.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Jul 24 2007

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

%E Simpler definition from _Wesley Ivan Hurt_, Mar 26 2014