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%I A264852 #18 Feb 16 2025 08:33:27
%S A264852 0,1,22,100,290,665,1316,2352,3900,6105,9130,13156,18382,25025,33320,
%T A264852 43520,55896,70737,88350,109060,133210,161161,193292,230000,271700,
%U A264852 318825,371826,431172,497350,570865,652240,742016,840752,949025,1067430,1196580,1337106
%N A264852 a(n) = n*(n + 1)*(n + 2)*(9*n - 7)/12.
%C A264852 Partial sums of 20-gonal (or icosagonal) pyramidal numbers. Therefore, this is the case k=9 of the general formula n*(n + 1)*(n + 2)*(k*n - k + 2)/12, which is related to 2*(k+1)-gonal pyramidal numbers.
%H A264852 OEIS Wiki, <a href="/load/view.php?a=aHR0cHM6Ly9vZWlzLm9yZy93aWtpL0ZpZ3VyYXRlX251bWJlcnM">Figurate numbers</a>
%H A264852 Eric Weisstein's World of Mathematics, <a href="/load/view.php?a=aHR0cHM6Ly9tYXRod29ybGQud29sZnJhbS5jb20vUHlyYW1pZGFsTnVtYmVyLmh0bWw">Pyramidal Number</a>
%H A264852 <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL2luZGV4L1JlYyNvcmRlcl8wNQ">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A264852 G.f.: x*(1 + 17*x)/(1 - x)^5.
%F A264852 a(n) = Sum_{k = 0..n} A172082(k).
%F A264852 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 A264852 Table[n (n + 1) (n + 2) (9 n - 7)/12, {n, 0, 50}]
%o A264852 (Magma) [n*(n+1)*(n+2)*(9*n-7)/12: n in [0..50]]; // _Vincenzo Librandi_, Nov 27 2015
%o A264852 (PARI) a(n)=n*(n+1)*(n+2)*(9*n-7)/12 \\ _Charles R Greathouse IV_, Jul 26 2016
%Y A264852 Cf. A172082.
%Y A264852 Cf. similar sequences with formula n*(n+1)*(n+2)*(k*n-k+2)/12 listed in A264850.
%K A264852 nonn,easy
%O A264852 0,3
%A A264852 _Ilya Gutkovskiy_, Nov 26 2015

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