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Number of integral points in a certain sequence of open quadrilaterals.
(Formerly M2529 N0997)
2

%I M2529 N0997 #38 May 02 2024 09:47:05

%S 0,0,1,3,6,9,13,18,24,31,39,47,56,66,77,89,102,115,129,144,160,177,

%T 195,213,232,252,273,295,318,341,365,390,416,443,471,499,528,558,589,

%U 621,654,687,721,756,792,829,867,905,944,984,1025,1067,1110

%N Number of integral points in a certain sequence of open 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="/A002578/b002578.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^3*(x^5+x^4+x^2+x+1)/((1-x^6)*(1-x)^2). - _Sean A. Irvine_, Apr 25 2017

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

%Y Cf. A002579.

%K nonn,easy

%O 1,4

%A _N. J. A. Sloane_

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