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A264852 a(n) = n*(n + 1)*(n + 2)*(9*n - 7)/12. 1

%I

%S 0,1,22,100,290,665,1316,2352,3900,6105,9130,13156,18382,25025,33320,

%T 43520,55896,70737,88350,109060,133210,161161,193292,230000,271700,

%U 318825,371826,431172,497350,570865,652240,742016,840752,949025,1067430,1196580,1337106

%N a(n) = n*(n + 1)*(n + 2)*(9*n - 7)/12.

%C 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 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 + 17*x)/(1 - x)^5.

%F a(n) = Sum_{k = 0..n} A172082(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) (n + 2) (9 n - 7)/12, {n, 0, 50}]

%o (MAGMA) [n*(n+1)*(n+2)*(9*n-7)/12: n in [0..50]]; // _Vincenzo Librandi_, Nov 27 2015

%o (PARI) a(n)=n*(n+1)*(n+2)*(9*n-7)/12 \\ _Charles R Greathouse IV_, Jul 26 2016

%Y Cf. A172082.

%Y Cf. similar sequences with formula n*(n+1)*(n+2)*(k*n-k+2)/12 listed in A264850.

%K nonn,easy

%O 0,3

%A _Ilya Gutkovskiy_, Nov 26 2015

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Last modified January 22 15:57 EST 2019. Contains 319364 sequences. (Running on oeis4.)