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A195041
Concentric heptagonal numbers.
8
0, 1, 7, 15, 28, 43, 63, 85, 112, 141, 175, 211, 252, 295, 343, 393, 448, 505, 567, 631, 700, 771, 847, 925, 1008, 1093, 1183, 1275, 1372, 1471, 1575, 1681, 1792, 1905, 2023, 2143, 2268, 2395, 2527, 2661, 2800, 2941, 3087, 3235, 3388, 3543
OFFSET
0,3
COMMENTS
A033582 and A069127 interleaved.
Partial sums of A047336. - Reinhard Zumkeller, Jan 07 2012
FORMULA
a(n) = 7*n^2/4 + 3*((-1)^n - 1)/8.
From R. J. Mathar, Sep 28 2011: (Start)
G.f.: -x*(1+5*x+x^2) / ( (1+x)*(x-1)^3 ).
a(n) + a(n+1) = A069099(n+1). (End)
a(n) = n^2 + floor(3*n^2/4). - Bruno Berselli, Aug 08 2013
Sum_{n>=1} 1/a(n) = Pi^2/42 + tan(sqrt(3/7)*Pi/2)*Pi/sqrt(21). - Amiram Eldar, Jan 16 2023
MATHEMATICA
CoefficientList[Series[-((x (1+5 x+x^2))/((-1+x)^3 (1+x))), {x, 0, 80}], x] (* or *) LinearRecurrence[{2, 0, -2, 1}, {0, 1, 7, 15}, 80] (* Harvey P. Dale, Jan 18 2021 *)
PROG
(Magma) [7*n^2/4+3*((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011
(Haskell)
a195041 n = a195041_list !! n
a195041_list = scanl (+) 0 a047336_list
-- Reinhard Zumkeller, Jan 07 2012
(PARI) a(n)=7*n^2\4 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 27 2011
STATUS
approved