A002579 Number of integral points in a certain sequence of closed quadrilaterals. (Formerly M2440 N0967)

3, 5, 8, 12, 17, 23, 30, 37, 45, 54, 64, 75, 87, 99, 112, 126, 141, 157, 174, 191, 209, 228, 248, 269, 291, 313, 336, 360, 385, 411, 438, 465, 493, 522, 552, 583, 615, 647, 680, 714, 749, 785, 822, 859, 897, 936, 976, 1017, 1059, 1101, 1144

Offset

1,1

References

Eugene Ehrhart, Deux corollaires de la loi de réciprocité du polyèdre rationnel. C. R. Acad. Sci. Paris Ser. A-B 265, 1967, A160-A162.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

E. Ehrhart, Deux corollaires de la loi de réciprocité du polyèdre rationnel, C. R. Acad. Sci. Paris Ser. A-B 265, 1967, A160-A162. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,1,-2,1).

Formula

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

G.f.: (x^5+x^4+x^3+x+1)/((1-x^6)*(1-x)^2). - Sean A. Irvine, Apr 25 2017

Mathematica

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 *)

Crossrefs

Cf. A002578.

Sequence in context: A241567 A131674 A095173 * A023544 A133263 A238531

Adjacent sequences: A002576 A002577 A002578 * A002580 A002581 A002582

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Apr 25 2017

Status

approved