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A154600
a(n) = 2*n^2 + 22*n + 9.
2
33, 61, 93, 129, 169, 213, 261, 313, 369, 429, 493, 561, 633, 709, 789, 873, 961, 1053, 1149, 1249, 1353, 1461, 1573, 1689, 1809, 1933, 2061, 2193, 2329, 2469, 2613, 2761, 2913, 3069, 3229, 3393, 3561, 3733, 3909, 4089, 4273, 4461, 4653, 4849, 5049, 5253
OFFSET
1,1
COMMENTS
Eleventh diagonal of A144562.
2*a(n) + 103 is a square.
FORMULA
From Vincenzo Librandi, Feb 26 2012: (Start)
G.f: x*(33 - 38*x + 9*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
Sum_{n>=1} 1/a(n) = 257162/3084939 + tan(sqrt(103)*Pi/2)*Pi/(2*sqrt(103)). - Amiram Eldar, Feb 25 2023
E.g.f.: -9 + (9 + 24*x + 2*x^2)*exp(x). - G. C. Greubel, May 30 2024
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {33, 61, 93}, 50] (* Vincenzo Librandi, Feb 26 2012 *)
4*Binomial[Range[50]+6, 2] - 51 (* G. C. Greubel, May 30 2024 *)
PROG
(PARI) a(n)=2*n*(n+22)+9 \\ Charles R Greathouse IV, Jan 11 2012
(Magma) I:=[33, 61, 93]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 26 2012
(SageMath) [2*n^2+22*n+9 for n in range(1, 51)] # G. C. Greubel, May 30 2024
CROSSREFS
Cf. A144562.
Sequence in context: A043983 A080673 A140156 * A100593 A115160 A053179
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 12 2009
STATUS
approved