A113338 Positive integers of the form (18*m^2+1)/11.

41, 59, 419, 473, 1193, 1283, 2363, 2489, 3929, 4091, 5891, 6089, 8249, 8483, 11003, 11273, 14153, 14459, 17699, 18041, 21641, 22019, 25979, 26393, 30713, 31163, 35843, 36329, 41369, 41891, 47291, 47849, 53609, 54203, 60323, 60953

Offset: 1

Author

Zak Seidov, Jan 08 2006

Keywords

• nonn
• easy

Comments

Here m=(11*(2*n-1)-9*(-1)^n)/4 for n>0.

(18*m^2 + 1)/11 is an integer for m=5+11k and m=6+11k, k=0,1,2,.... [ Corrected by Bruno Berselli, Jun 28 2010]

Links

• Bruno Berselli, Table of n, a(n) for n = 1..10000.
• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A179088, A179337, A179338, A179339, A179370.

Programs

PARI

a(n)=(198*n*(n-1)-81*(2*n-1)*(-1)^n+83)/4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

From Bruno Berselli, Jun 29 2010: (Start)

G.f.: x*(41+18*x+278*x^2+18*x^3+41*x^4)/((1+x)^2*(1-x)^3).

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

a(n) = (198*n*(n-1)-81*(2*n-1)*(-1)^n+83)/4. (End)

Extensions

Definition corrected, comment and cross-reference added by Bruno Berselli, Jul 13 2010