%I M2440 N0967 #30 May 02 2024 04:31:59

%S 3,5,8,12,17,23,30,37,45,54,64,75,87,99,112,126,141,157,174,191,209,

%T 228,248,269,291,313,336,360,385,411,438,465,493,522,552,583,615,647,

%U 680,714,749,785,822,859,897,936,976,1017,1059,1101,1144

%N Number of integral points in a certain sequence of closed quadrilaterals.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A002579/b002579.txt">Table of n, a(n) for n = 1..1000</a>

%H Eugène Ehrhart, <a href="https://gallica.bnf.fr/ark:/12148/bpt6k6236329w/f174.item">Deux corollaires de la loi de réciprocité du polyèdre rationnel</a>, C. R. Acad. Sci. Paris Ser. A 265, 1967, 160-162.

%H Eugène Ehrhart, <a href="/A002578/a002578.pdf">Deux corollaires de la loi de réciprocité du polyèdre rationnel</a>, C. R. Acad. Sci. Paris Ser. A 265, 1967, 160-162. [Annotated scanned copy]

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1,0,0,0,1,-2,1).

%F Ehrhart (1967) gives a g.f. on page 161.

%F G.f.: (x^5+x^4+x^3+x+1)/((1-x^6)*(1-x)^2). - _Sean A. Irvine_, Apr 25 2017

%t Rest[CoefficientList[Series[(x^5 + x^4 + x^3 + x + 1) / ((1 - x^6) (1 - x)^2), {x, 0, 40}], x]] (* _Vincenzo Librandi_, Apr 26 2017 *)

%Y Cf. A002578.

%K nonn,easy

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Apr 25 2017