|
%I #38 Sep 08 2022 08:46:01
%S 2,9,23,44,72,107,149,198,254,317,387,464,548,639,737,842,954,1073,
%T 1199,1332,1472,1619,1773,1934,2102,2277,2459,2648,2844,3047,3257,
%U 3474,3698,3929,4167,4412,4664,4923,5189,5462
%N a(n) = (7*n^2 - 7*n + 4)/2.
%C a(n) is the sum of the n-th centered triangular number and n-th centered square number.
%C Difference of consecutive terms gives A008589 (multiples of 7).
%H G. C. Greubel, <a href="/A209294/b209294.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = (7*n^2 - 7*n + 4) = 7*T(n) + 2 with T = A000217.
%F G.f.: x*(2+3*x+2*x^2)/(1-x)^3. - _Bruno Berselli_, Jan 18 2013
%F a(n) = a(-n+1) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Bruno Berselli_, Jan 18 2013
%F a(n) = 1 + A069099(n). - _Omar E. Pol_, Apr 27 2017
%F E.g.f.: ((7*x^2 + 4)*exp(x) - 4)/2. - _G. C. Greubel_, Jan 04 2018
%t Table[(7*n^2 - 7*n + 4)/2, {n, 1, 50}] (* _G. C. Greubel_, Jan 04 2018 *)
%t LinearRecurrence[{3,-3,1},{2,9,23},40] (* _Harvey P. Dale_, Nov 02 2020 *)
%o (PARI) a(n)=7*n*(n-1)/2+2 \\ _Charles R Greathouse IV_, Jan 17 2013
%o (Magma) [(7*n^2 - 7*n + 4)/2: n in [1..30]]; // _G. C. Greubel_, Jan 04 2018
%Y Cf. A000217, A005448, A001844, A008589.
%K nonn,easy
%O 1,1
%A _Marco Piazzalunga_, Jan 17 2013
|
