A002797 Number of solutions to a linear inequality. (Formerly M1360 N0524)

3, 2, 5, 9, 17, 27, 40, 55, 73, 94, 117, 143, 171, 203, 236, 273, 311, 354, 397, 445, 493, 547, 600, 659, 717, 782, 845, 915, 983, 1059, 1132, 1213, 1291, 1378, 1461, 1553, 1641, 1739, 1832, 1935, 2033, 2142, 2245, 2359, 2467, 2587, 2700

Offset

0,1

References

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

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

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

E. Ehrhart, Sur un problème de géométrie diophantienne linéaire I, (Polyèdres et réseaux), J. Reine Angew. Math. 226 1967 1-29. MR0213320 (35 #4184). [Annotated scanned copy of pages 16 and 22 only]

E. Ehrhart, Sur un problème de géométrie diophantienne linéaire II. Systèmes diophantiens linéaires, J. Reine Angew. Math. 227 1967 25-49. [Annotated scanned copy of pages 47-49 only]

E. Ehrhart, Sur un problème de géométrie diophantienne linéaire II. Systèmes diophantiens linéaires, J. Reine Angew. Math. 227 1967 25-49.

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

Formula

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

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

Mathematica

LinearRecurrence[{1, 1, -1, 1, -1, -1, 1}, {3, 2, 5, 9, 17, 27, 40}, 50] (* Harvey P. Dale, Feb 06 2026 *)

Prog

(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

Crossrefs

Sequence in context: A193796 A249906 A258930 * A049920 A257981 A128914

Adjacent sequences: A002794 A002795 A002796 * A002798 A002799 A002800

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Initial term, missing a(9), and more terms from Sean A. Irvine, Aug 20 2014

Status

approved