A256718 - OEIS

%I #21 Jan 15 2024 13:44:34

%S 0,1,24,90,220,435,756,1204,1800,2565,3520,4686,6084,7735,9660,11880,

%T 14416,17289,20520,24130,28140,32571,37444,42780,48600,54925,61776,

%U 69174,77140,85695,94860,104656,115104,126225,138040,150570,163836,177859,192660

%N a(n) = n*(n+1)*(7*n-6)/2.

%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (21st row of the table).

%H Bruno Berselli, <a href="/A256718/b256718.txt">Table of n, a(n) for n = 0..1000</a>

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

%F G.f.: x*(1 + 20*x)/(1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) with n>3, a(0)=0, a(1)=1, a(2)=24, a(3)=90.

%F a(n) = Sum_{i=0..n-1} (n-i)*(21*i+1) for n>0.

%t Table[n (n + 1) (7 n - 6)/2, {n, 0, 40}]

%t LinearRecurrence[{4,-6,4,-1},{0,1,24,90},40] (* _Harvey P. Dale_, Jan 15 2024 *)

%o (PARI) vector(40, n, n--; n*(n+1)*(7*n-6)/2)

%o (Sage) [n*(n+1)*(7*n-6)/2 for n in (0..40)]

%o (Magma) [n*(n+1)*(7*n-6)/2: n in [0..40]];

%Y Partial sums of A051875.

%Y Cf. similar sequences listed in A237616.

%K nonn,easy

%O 0,3

%A _Bruno Berselli_, Apr 09 2015