A002578 Number of integral points in a certain sequence of open quadrilaterals. (Formerly M2529 N0997)

0, 0, 1, 3, 6, 9, 13, 18, 24, 31, 39, 47, 56, 66, 77, 89, 102, 115, 129, 144, 160, 177, 195, 213, 232, 252, 273, 295, 318, 341, 365, 390, 416, 443, 471, 499, 528, 558, 589, 621, 654, 687, 721, 756, 792, 829, 867, 905, 944, 984, 1025, 1067, 1110

Offset

1,4

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

Mathematica

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 *)

Crossrefs

Cf. A002579.

Sequence in context: A132352 A033436 A059293 * A129728 A307270 A310160

Adjacent sequences: A002575 A002576 A002577 * A002579 A002580 A002581

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Apr 25 2017

Status

approved