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A273366
a(n) = 10*n^2 + 10*n + 2.
7
2, 22, 62, 122, 202, 302, 422, 562, 722, 902, 1102, 1322, 1562, 1822, 2102, 2402, 2722, 3062, 3422, 3802, 4202, 4622, 5062, 5522, 6002, 6502, 7022, 7562, 8122, 8702, 9302, 9922, 10562, 11222, 11902, 12602, 13322, 14062, 14822, 15602
OFFSET
0,1
COMMENTS
These are the numbers k such that 10*k+5 is a perfect square.
FORMULA
G.f.: 2*(x^2+8x+1)/(1-x)^3.
From G. C. Greubel, May 20 2016: (Start)
E.g.f.: 2*(1 + 10*x + 5*x^2)*exp(x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
a(n) = 2*A062786(n+1). - R. J. Mathar, Jun 03 2016
Sum_{n>=0} 1/a(n) = Pi/(2*sqrt(5)) * tan(Pi/(2*sqrt(5))) (A350760). - Amiram Eldar, Jan 20 2022
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {2, 22, 62}, 50] (* G. C. Greubel, May 20 2016 *)
Table[10n^2+10n+2, {n, 0, 40}] (* Harvey P. Dale, May 21 2024 *)
PROG
(PARI) a(n)=10*n^2+10*n+2 \\ Charles R Greathouse IV, Jan 31 2017
CROSSREFS
Cf. A033583 (perfect squares ending in 0 in base 10 with final 0 removed).
Sequence in context: A168669 A271883 A152995 * A053940 A156480 A348488
KEYWORD
nonn,easy
AUTHOR
STATUS
approved