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%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
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