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A195041 Concentric heptagonal numbers. 8

%I

%S 0,1,7,15,28,43,63,85,112,141,175,211,252,295,343,393,448,505,567,631,

%T 700,771,847,925,1008,1093,1183,1275,1372,1471,1575,1681,1792,1905,

%U 2023,2143,2268,2395,2527,2661,2800,2941,3087,3235,3388,3543

%N Concentric heptagonal numbers.

%C A033582 and A069127 interleaved.

%C Partial sums of A047336. - _Reinhard Zumkeller_, Jan 07 2012

%H Vincenzo Librandi, <a href="/A195041/b195041.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

%F a(n) = 7*n^2/4 + 3*((-1)^n - 1)/8.

%F From _R. J. Mathar_, Sep 28 2011: (Start)

%F G.f.: -x*(1+5*x+x^2) / ( (1+x)*(x-1)^3 ).

%F a(n) + a(n+1) = A069099(n+1). (End)

%F a(n) = n^2 + floor(3*n^2/4). - _Bruno Berselli_, Aug 08 2013

%o (MAGMA) [7*n^2/4+3*((-1)^n-1)/8: n in [0..50]]; // _Vincenzo Librandi_, Sep 29 2011

%o (Haskell)

%o a195041 n = a195041_list !! n

%o a195041_list = scanl (+) 0 a047336_list

%o -- _Reinhard Zumkeller_, Jan 07 2012

%o (PARI) a(n)=7*n^2\4 \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Column 7 of A195040.

%Y Cf. A032527, A032528, A077221, A195042.

%K nonn,easy

%O 0,3

%A _Omar E. Pol_, Sep 27 2011

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Last modified October 18 00:21 EDT 2019. Contains 328135 sequences. (Running on oeis4.)