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A017174
a(n) = (9*n + 1)^2.
11
1, 100, 361, 784, 1369, 2116, 3025, 4096, 5329, 6724, 8281, 10000, 11881, 13924, 16129, 18496, 21025, 23716, 26569, 29584, 32761, 36100, 39601, 43264, 47089, 51076, 55225, 59536, 64009, 68644
OFFSET
0,2
FORMULA
G.f.: x*(1 + 97*x + 64*x^2)/(1-x)^3. - Bruno Berselli, Aug 25 2011
From G. C. Greubel, Dec 28 2022: (Start)
a(2*n) = A016754(9*n).
a(2*n+1) = 4*A017222(n).
E.g.f.: (1 + 99*x + 81*x^2)*exp(x). (End)
MATHEMATICA
(9*Range[0, 40] +1)^2 (* G. C. Greubel, Dec 28 2022 *)
LinearRecurrence[{3, -3, 1}, {1, 100, 361}, 50] (* Harvey P. Dale, Feb 25 2024 *)
PROG
(Magma) [(9*n+1)^2: n in [0..40]]; // Vincenzo Librandi, Aug 25 2011
(PARI) a(n)=(9*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017
(SageMath) [(9*n+1)^2 for n in range(41)] # G. C. Greubel, Dec 28 2022
CROSSREFS
Sequences of the form (m*n+1)^2: A000012 (m=0), A000290 (m=1), A016754 (m=2), A016778 (m-3), A016814 (m=4), A016862 (m=5), A016922 (m=6), A016994 (m=7), A017078 (m=8), this sequence (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).
Cf. A017222.
Sequence in context: A124437 A349181 A138668 * A202334 A250806 A250853
KEYWORD
nonn,easy
STATUS
approved