A106388 Numbers k such that 11k = 6j^2 + 6j + 1.

11, 23, 131, 167, 383, 443, 767, 851, 1283, 1391, 1931, 2063, 2711, 2867, 3623, 3803, 4667, 4871, 5843, 6071, 7151, 7403, 8591, 8867, 10163, 10463, 11867, 12191, 13703, 14051, 15671, 16043, 17771, 18167, 20003, 20423, 22367, 22811, 24863, 25331, 27491, 27983

Offset: 1

Author

Pierre CAMI, May 01 2005

Keywords

• nonn
• easy

Comments

j sequence = A106387

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A106387, A106389, A106390.

Programs

Mathematica

LinearRecurrence[{1,2,-2,-1,1},{11,23,131,167,383},50] (* Harvey P. Dale, Jul 26 2018 *)

PARI

Vec((11+12*x+86*x^2+12*x^3+11*x^4)/(1+x)^2/(1-x)^3+O(x^99)) \\ Charles R Greathouse IV, Dec 28 2011

Formula

a(1)=11, a(2)=23; if n odd a(n)=a(n-1)+54*(n-1), if n even a(n)=a(n-1)+12*(n-1).

a(n) = (66*n*(n-1)-21*(2*n-1)*(-1)^n+23)/4.

G.f.: x*(11+12*x+86*x^2+12*x^3+11*x^4)/((1+x)^2*(1-x)^3).

a(n)-a(n-1)-2*a(n-2)+2*a(n-3)+a(n-4)-a(n-5) = 0 for n>5.

Extensions

Formulae corrected and added by Bruno Berselli, Nov 16 2010

More terms from Colin Barker, Apr 16 2014