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

Author

Omar E. Pol, Sep 27 2011

Keywords

• nonn
• easy

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).

Crossrefs

Column 7 of A195040.

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

Programs

Haskell

a195041 n = a195041_list !! n
a195041_list = scanl (+) 0 a047336_list
-- Reinhard Zumkeller, Jan 07 2012

Magma

[7*n^2/4+3*((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 29 2011

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 *)

PARI

a(n)=7*n^2\4 \\ Charles R Greathouse IV, Oct 07 2015

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