A002797 Number of solutions to a linear inequality.

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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. Systemes diophantiens lineaires, J. Reine Angew. Math. 227 1967 25-49. [Annotated scanned copy of pages 47-49 only]
• Ehrhart, E.; Sur un problème de géométrie diophantienne linéaire II. Systemes diophantiens lineaires, J. Reine Angew. Math. 227 1967 25-49.
• Index entries for linear recurrences with constant coefficients, signature (1, 1, -1, 1, -1, -1, 1).

Programs

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

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

Extensions

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