A011918 a(n) = A011916(n) + A011922(n) - 1.

5, 76, 1065, 14840, 206701, 2878980, 40099025, 558507376, 7779004245, 108347552060, 1509086724601, 21018866592360, 292755045568445, 4077551771365876, 56792969753553825, 791024024778387680, 11017543377143873701, 153454583255235844140, 2137346622196157944265

Offset: 1

Author

Mario Velucchi (mathchess(AT)velucchi.it)

Keywords

• nonn
• easy

Comments

Also integers n such that n^2+(n+1)^2 is equal to the sum of two consecutive octagonal numbers. - Colin Barker, Dec 20 2014

References

• Mario Velucchi, "Seeing couples", Recreational and Educational Computing, to appear 1997. [apparently never materialized, Joerg Arndt, Aug 14 2013]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (15,-15,1).

Crossrefs

Cf. A011916.

Programs

Mathematica

CoefficientList[Series[-(5 + x) / ((x - 1) (x^2 - 14 x + 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 13 2013 *)

PARI

Vec(-x*(5+x)/((x-1)*(x^2-14*x+1)) + O(x^100)) \\ Colin Barker, Dec 20 2014

Formula

a(n) = +15*a(n-1) -15*a(n-2) +a(n-3). G.f.: -x*(5+x)/ ((x-1) * (x^2-14*x+1)). - R. J. Mathar, Apr 15 2010

a(n) = (A007655(n+2) - 3*A007655(n+1) - 1)/2. - Ralf Stephan, Aug 13 2013

a(n) = (-6-(7-4*sqrt(3))^n*(-3+sqrt(3))+(3+sqrt(3))*(7+4*sqrt(3))^n)/12. - Colin Barker, Mar 05 2016

Extensions

More terms from R. J. Mathar, Apr 15 2010