This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A198148 #52 May 02 2025 17:05:42
%S A198148 0,3,1,15,3,35,6,63,10,99,15,143,21,195,28,255,36,323,45,399,55,483,
%T A198148 66,575,78,675,91,783,105,899,120,1023,136,1155,153,1295,171,1443,190,
%U A198148 1599,210,1763,231,1935,253,2115,276,2303,300,2499,325
%N A198148 a(n) = n*(n+2)*(9 - 7*(-1)^n)/16.
%C A198148 See, in A181318(n), A060819(n)*A060819(n+p): A060819(n)^2, A064038(n), a(n), A160050(n), A061037(n), A178242(n). The second differences a(n+2)-2*a(n+1)+a(n) = -5, 16, -26, 44, -61, 86, -110, 142, -173, 212, -250, 296, -341, 394, -446, 506, taken modulo 9 are periodic with the palindromic period 4, 7, 1, 8, 2, 5, 7, 7, 7, 5, 2, 8, 1, 7, 4.
%H A198148 Vincenzo Librandi, <a href="/A198148/b198148.txt">Table of n, a(n) for n = 0..10000</a>
%H A198148 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A198148 a(n) = A060819(n)*A060819(n+2).
%F A198148 a(2n) = n*(n+1)/2 = A000217(n).
%F A198148 a(2n+1) = (2*n+1)*(2*n+3) = A000466(n+1).
%F A198148 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6), n>5.
%F A198148 a(n+1) - a(n) = (7*(-1)^n *(2*n^2+6*n+3) +18*n +27)/16.
%F A198148 a(n) = A142705(n) / A000034(n+1).
%F A198148 a(n) = A005563(n) / A010689(n+1). - _Franklin T. Adams-Watters_, Oct 21 2011
%F A198148 G.f. x*(3 +x +6*x^2 -x^4)/(1-x^2)^3. - _R. J. Mathar_, Oct 25 2011
%F A198148 a(n)*a(n+1) = a(A028552(n)) = A050534(n+2). - _Bruno Berselli_, Oct 26 2011
%F A198148 a(n) = numerator( binomial((n+2)/2,2) ). - _Wesley Ivan Hurt_, Oct 16 2013
%F A198148 E.g.f.: x*((24+x)*cosh(x) + (3+8*x)*sinh(x))/8. - _G. C. Greubel_, Sep 20 2018
%F A198148 Sum_{n>=1} 1/a(n) = 5/2. - _Amiram Eldar_, Aug 12 2022
%p A198148 A198148:=n->n*(n+2)*(9-7*(-1)^n)/16; seq(A198148(k), k=0..100); # _Wesley Ivan Hurt_, Oct 16 2013
%t A198148 LinearRecurrence[{0,3,0,-3,0,1},{0,3,1,15,3,35},60] (* _Vincenzo Librandi_, Nov 25 2011 *)
%o A198148 (Magma) [n*(n+2)*(9-7*(-1)^n)/16: n in [0..60]]; // _Vincenzo Librandi_, Nov 25 2011
%o A198148 (PARI) a(n)=n*(n+2)*(9-7*(-1)^n)/16 \\ _Charles R Greathouse IV_, Oct 16 2015
%o A198148 (Sage) [n*(n+2)*(9-7*(-1)^n)/16 for n in (0..60)] # _G. C. Greubel_, Feb 21 2019
%o A198148 (GAP) List([0..60], n -> n*(n+2)*(9-7*(-1)^n)/16); # _G. C. Greubel_, Feb 21 2019
%Y A198148 Cf. quadrisections A014105, A001539, A000384, A141759.
%Y A198148 Cf. A060819, A000217, A000466, A142705, A000034, A005563, A010689, A028552, A050534.
%K A198148 nonn,easy
%O A198148 0,2
%A A198148 _Paul Curtz_, Oct 21 2011