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%I #39 Sep 08 2022 08:46:04
%S 1,13,40,82,139,211,298,400,517,649,796,958,1135,1327,1534,1756,1993,
%T 2245,2512,2794,3091,3403,3730,4072,4429,4801,5188,5590,6007,6439,
%U 6886,7348,7825,8317,8824,9346,9883,10435,11002,11584,12181,12793,13420,14062
%N a(n) = (15*n^2 + 9*n + 2)/2.
%C Sequence related to the heptagonal numbers (A000566) by a(n) = n*A000566(n)-(n-1)*A000566(n-1).
%C Other similar sequences:
%C A005408(m) = (m+1)*A001477(m+1)-m*A001477(m), A001477 = nonn. integers;
%C A000326(m) = m*A000217(n)-(m-1)*A000217(m-1), A000217 = triangular numbers;
%C A003215(m) = (m+1)*A000290(m+1)-n*A000290(m), A000290 = square numbers;
%C A081267(m) = (m+1)*A000326(m+1)-n*A000326(m), A000326 = pentagonal numbers;
%C A080859(m) = (m+1)*A000384(m+1)-n*A000384(m), A000384 = hexagonal numbers;
%C A214675(m) = m*A000567(m)-(m-1)*A000567(m-1), A000567 = octagonal numbers.
%H Bruno Berselli, <a href="/A220083/b220083.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: (1+10*x+4*x^2)/(1-x)^3.
%F Sum( a(i), i=0..n ) = A006597(n+1).
%F a(n) + a(-n) = A010005(n) for n>0.
%p A220083:=n->(15*n^2 + 9*n + 2)/2; seq(A220083(n), n=0..100); # _Wesley Ivan Hurt_, Nov 14 2013
%t Table[(15 n^2 + 9 n + 2)/2, {n, 0, 45}]
%t CoefficientList[Series[(1 + 10 x + 4 x^2) / (1 - x)^3, {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)
%o (Magma) /* By first comment: */ A000566:=func<n | n*(5*n-3)/2>; [n*A000566(n)-(n-1)*A000566(n-1): n in [1..45]];
%o (Magma) [(15*n^2 + 9*n + 2)/2: n in [0..50]]; // _Vincenzo Librandi_, Aug 18 2013
%o (Maxima) A220083(n):=(15*n^2 + 9*n + 2)/2$ makelist(A220083(n),n,0,20); /* _Martin Ettl_, Dec 11 2012 */
%o (PARI) a(n)=(15*n^2+9*n+2)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A000326, A003215, A005408, A006597, A080859, A081267, A214675.
%K nonn,easy
%O 0,2
%A _Bruno Berselli_, Dec 10 2012
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