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A179338
Positive integers of the form (10*m^2+1)/11.
5
1, 91, 131, 401, 481, 931, 1051, 1681, 1841, 2651, 2851, 3841, 4081, 5251, 5531, 6881, 7201, 8731, 9091, 10801, 11201, 13091, 13531, 15601, 16081, 18331, 18851, 21281, 21841, 24451, 25051, 27841, 28481, 31451, 32131, 35281, 36001, 39331
OFFSET
1,2
COMMENTS
Here m=(11*(2*n-1)+7*(-1)^n)/4 for n>0.
FORMULA
a(n) = (110*n*(n-1)+35*(2*n-1)*(-1)^n+39)/4.
G.f.: x*(1+90*x+38*x^2+90*x^3+1*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).
MATHEMATICA
Select[(10Range[300]^2+1)/11, IntegerQ] (* or *) LinearRecurrence[ {1, 2, -2, -1, 1}, {1, 91, 131, 401, 481}, 50] (* Harvey P. Dale, Jul 10 2014 *)
PROG
(PARI) isok(n) = (((11*n-1) % 10 == 0) && issquare((11*n-1)/10)) \\ Michel Marcus, Jun 07 2013
(Magma) [(110*n*(n-1)+35*(2*n-1)*(-1)^n+39)/4: n in [1..50]]; // Vincenzo Librandi, Jul 10 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jul 11 2010
STATUS
approved