A256716 - OEIS

%I #28 Sep 08 2022 08:46:11

%S 0,1,25,94,230,455,791,1260,1884,2685,3685,4906,6370,8099,10115,12440,

%T 15096,18105,21489,25270,29470,34111,39215,44804,50900,57525,64701,

%U 72450,80794,89755,99355,109616,120560,132209,144585,157710,171606,186295,201799

%N a(n) = n*(n+1)*(22*n-19)/6.

%C This sequence is related to the tridecagonal numbers (A051865) by a(n) = n*A051865(n) - Sum_{i=0..n-1} A051865(i).

%D E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (22nd row of the table).

%H Bruno Berselli, <a href="/A256716/b256716.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 + 21*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)=25, a(3)=94.

%F a(n) = Sum_{i=0..n-1} (n-i)*(22*i+1) for n>0.

%t Table[n (n + 1) (22 n - 19)/6, {n, 0, 40}]

%o (PARI) vector(40, n, n--; n*(n+1)*(22*n-19)/6)

%o (Sage) [n*(n+1)*(22*n-19)/6 for n in (0..40)]

%o (Magma) [n*(n+1)*(22*n-19)/6: n in [0..40]];

%Y Partial sums of A051876.

%Y Cf. similar sequences listed in A237616.

%Y Cf. A051865.

%K nonn,easy

%O 0,3

%A _Bruno Berselli_, Apr 09 2015