A086640 Arrange n^2 octagons that each have area 7 so that they leave (n-1)^2 square gaps each with area 2; a(n) is the total area of these polygons.

7, 30, 71, 130, 207, 302, 415, 546, 695, 862, 1047, 1250, 1471, 1710, 1967, 2242, 2535, 2846, 3175, 3522, 3887, 4270, 4671, 5090, 5527, 5982, 6455, 6946, 7455, 7982, 8527, 9090, 9671, 10270, 10887, 11522, 12175, 12846, 13535, 14242, 14967, 15710

Offset

1,1

References

Keith Devlin, "The language of mathematics", Henry Holt, NY, plate 9 after p. 249.

Links

Table of n, a(n) for n=1..42.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 9n^2-4n+2.

G.f. -x*(2*x+7)*(1+x) / (x-1)^3 . - R. J. Mathar, Sep 15 2012

Prog

(PARI) a(n)=9*n^2-4*n+2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Sequence in context: A063148 A116283 A139274 * A083474 A030440 A256225

Adjacent sequences: A086637 A086638 A086639 * A086641 A086642 A086643

Keyword

nonn,easy,less

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jul 26 2003

Extensions

Edited and extended by David Wasserman, Jun 20 2007

Status

approved