A106058 - OEIS

%I #33 Jan 05 2025 19:51:38

%S 0,0,0,2,9,22,42,70,107,154,212,282,365,462,574,702,847,1010,1192,

%T 1394,1617,1862,2130,2422,2739,3082,3452,3850,4277,4734,5222,5742,

%U 6295,6882,7504,8162,8857,9590,10362,11174,12027,12922,13860,14842,15869,16942,18062

%N 4th diagonal of triangle in A059317.

%H W. F. Klostermeyer, M. E. Mays, L. Soltes and G. Trapp, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/35-4/klostermeyer.pdf">A Pascal rhombus</a>, Fibonacci Quarterly, 35 (1997), 318-328.

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

%F For n>1, a(n) = (1/6)*(n-2)*(n^2 + 8n - 21).

%F From _R. J. Mathar_, Feb 06 2010: (Start)

%F a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4) for n >= 6.

%F G.f.: -x^3*(-2-x+2*x^2)/(x-1)^4. (End)

%t Join[{0,0}, LinearRecurrence[{4, -6, 4, -1}, {0, 2, 9, 22}, 45]] (* _Georg Fischer_, Dec 10 2019 *)

%o (PARI) a(n)=if(n>2,(n-2)*(n^2 + 8*n - 21)/6,0) \\ _Charles R Greathouse IV_, Oct 18 2022

%Y Cf. A007290, A059317.

%K nonn,easy

%O 0,4

%A _N. J. A. Sloane_, May 28 2005