A016994 - OEIS

%I #26 May 07 2024 06:29:47

%S 1,64,225,484,841,1296,1849,2500,3249,4096,5041,6084,7225,8464,9801,

%T 11236,12769,14400,16129,17956,19881,21904,24025,26244,28561,30976,

%U 33489,36100,38809,41616,44521,47524

%N a(n) = (7*n + 1)^2.

%H Vincenzo Librandi, <a href="/A016994/b016994.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: (1 + 61*x + 36*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jan 27 2013

%F From _G. C. Greubel_, Dec 28 2022: (Start)

%F a(2*n) = A134934(n).

%F a(2*n+1) = 4*A017030(n).

%F E.g.f.: (1 + 63*x + 49*x^2)*exp(x). (End)

%F Sum_{n>=0} 1/a(n) = Psi'(1/7)/49 =  1.027703498712483534.. - _R. J. Mathar_, May 07 2024

%t (7Range[0,50]+1)^2  (* _Harvey P. Dale_, Mar 05 2011 *)

%t CoefficientList[Series[(1+61*x+36*x^2)/(1-x)^3, {x,0,40}], x] (* _Vincenzo Librandi_, Jan 27 2013 *)

%o (Magma) [(7*n+1)^2: n in [0..40]]; // _Vincenzo Librandi_, Jul 13 2011

%o (PARI) a(n)=(7*n+1)^2 \\ _Charles R Greathouse IV_, Jun 17 2017

%o (SageMath) [(7*n+1)^2 for n in range(41)] # _G. C. Greubel_, Dec 28 2022

%Y 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), this sequence (m=7), A017078 (m=8), A017174 (m=9), A017282 (m=10), A017402 (m=11), A017534 (m=12), A134934 (m=14).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_