A264854 - OEIS

%I #19 Sep 08 2022 08:46:14

%S 0,1,14,61,175,400,791,1414,2346,3675,5500,7931,11089,15106,20125,

%T 26300,33796,42789,53466,66025,80675,97636,117139,139426,164750,

%U 193375,225576,261639,301861,346550,396025,450616,510664,576521,648550,727125,812631,905464,1006031

%N a(n) = n*(n + 1)*(11*n^2 + 11*n - 10)/24.

%C Partial sums of centered 11-gonal (or hendecagonal) pyramidal numbers.

%H OEIS Wiki, <a href="https://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PyramidalNumber.html">Pyramidal Number</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

%F G.f.: x*(1 + 9*x + x^2)/(1 - x)^5.

%F a(n) = Sum_{k = 0..n} A004467(k).

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Vincenzo Librandi_, Nov 27 2015

%t Table[n (n + 1) (11 n^2 + 11 n - 10)/24, {n, 0, 50}]

%o (Magma) [n*(n+1)*(11*n^2+11*n-10)/24: n in [0..50]]; // _Vincenzo Librandi_, Nov 27 2015

%o (PARI) a(n)=n*(n+1)*(11*n^2+11*n-10)/24 \\ _Charles R Greathouse IV_, Jul 26 2016

%Y Cf. A004467.

%Y Cf. similar sequences provided by the partial sums of centered k-gonal pyramidal numbers: A006522 (k=1), A006007 (k=2), A002817 (k=3), A006325 (k=4), A006322 (k=5), A000537 (k=6), A006323 (k=7), A006324 (k=8), A236770 (k=9), A264853 (k=10), this sequence (k=11), A062392 (k=12), A264888 (k=13).

%K nonn,easy

%O 0,3

%A _Ilya Gutkovskiy_, Nov 26 2015