A195041 Concentric heptagonal numbers.

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

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

Column 7 of A195040.

Cf. A032527, A032528, A033582, A047336, A069099, A069127, A077221, A195042.

Sequence in context: A239934 A193553 A274090 * A229462 A302125 A006188

Adjacent sequences: A195038 A195039 A195040 * A195042 A195043 A195044

Keyword

nonn,easy

Author

Omar E. Pol, Sep 27 2011

Status

approved