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A002797 Number of solutions to a linear inequality.

%I A002797 M1360 N0524 #27 Jun 25 2023 19:59:55
%S A002797 3,2,5,9,17,27,40,55,73,94,117,143,171,203,236,273,311,354,397,445,
%T A002797 493,547,600,659,717,782,845,915,983,1059,1132,1213,1291,1378,1461,
%U A002797 1553,1641,1739,1832,1935,2033,2142,2245,2359,2467,2587,2700
%N A002797 Number of solutions to a linear inequality.
%D A002797 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002797 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002797 Alois P. Heinz, <a href="/A002797/b002797.txt">Table of n, a(n) for n = 0..1000</a>
%H A002797 E. Ehrhart, <a href="/A002789/a002789.pdf">Sur un problème de géométrie diophantienne linéaire I, (Polyèdres et réseaux)</a>, J. Reine Angew. Math. 226 1967 1-29. MR0213320 (35 #4184). [Annotated scanned copy of pages 16 and 22 only]
%H A002797 E. Ehrhart, <a href="/A002789/a002789_1.pdf">Sur un problème de géométrie diophantienne linéaire II. Systemes diophantiens lineaires</a>, J. Reine Angew. Math. 227 1967 25-49. [Annotated scanned copy of pages 47-49 only]
%H A002797 Ehrhart, E.; <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN243919689_0227&amp;DMDID=DMDLOG_0005&amp;LOGID=LOG_0005&amp;PHYSID=PHYS_0053">Sur un problème de géométrie diophantienne linéaire II. Systemes diophantiens lineaires</a>, J. Reine Angew. Math. 227 1967 25-49.
%H A002797 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 1, -1, -1, 1).
%F A002797 a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) - a(n-5) - a(n-6) + a(n-7). - _Sean A. Irvine_, Aug 20 2014
%F A002797 G.f.: -(5*x^6+7*x^5+2*x^4+5*x^3-x+3)/((x^2+1)*(x+1)^2*(x-1)^3). - _Alois P. Heinz_, Aug 20 2014
%o A002797 (PARI) Vec(-(5*x^6+7*x^5+2*x^4+5*x^3-x+3)/((x^2+1)*(x+1)^2*(x-1)^3) + O(x^50)) \\ _Michel Marcus_, Jan 26 2015
%K A002797 nonn,easy
%O A002797 0,1
%A A002797 _N. J. A. Sloane_
%E A002797 Initial term, missing a(9), and more terms from _Sean A. Irvine_, Aug 20 2014