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A133092 Row sums of triangle A133091.

%I A133092 #24 Mar 07 2022 02:06:31
%S A133092 1,4,6,16,15,36,28,64,45,100,66,144,91,196,120,256,153,324,190,400,
%T A133092 231,484,276,576,325,676,378,784,435,900,496,1024,561,1156,630,1296,
%U A133092 703,1444,780,1600,861,1764,946,1936,1035,2116,1128,2304,1225,2500,1326,2704
%N A133092 Row sums of triangle A133091.
%C A133092 Even squares interleaved with hexagonal numbers, A000384, such that A000384(n), (n,odd) = A000384((n+1)/2).
%H A133092 Bruno Berselli, <a href="/A133092/b133092.txt">Table of n, a(n) for n = 1..1000</a>
%H A133092 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A133092 G.f.: x*(1 + 4*x + 3*x^2 + 4*x^3)/(1-x^2)^3. - _Philippe Deléham_, Mar 02 2012
%F A133092 a(n) = (n/4)*(3*n + (n-1)*(-1)^n + 1). - _Bruno Berselli_, Mar 02 2012
%F A133092 E.g.f.: (x/4)*(x*exp(-x) + (4 + 3*x)*exp(x)). - _G. C. Greubel_, Oct 21 2017
%F A133092 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6). - _Wesley Ivan Hurt_, Jun 08 2021
%e A133092 a(4) = 16 = sum of row 4 terms of triangle A133091: (2 + 4 + 6 + 4).
%e A133092 a(4) = 16 = 4^2.
%e A133092 a(7) = 28 = A000384(4), where A000384 = (1, 6, 15, 28, 45, 66, 91, ...).
%t A133092 Table[(n/4)*(3*n + (n - 1)*(-1)^n + 1), {n, 48}] (* _Bruno Berselli_, Mar 02 2012 *)
%o A133092 (PARI) for(n=1,50, print1((n/4)*(3*n+(n-1)*(-1)^n+1), ", ")) \\ _G. C. Greubel_, Oct 21 2017
%o A133092 (Magma) [(n/4)*(3*n+(n-1)*(-1)^n+1): n in [1..50]]; // _G. C. Greubel_, Oct 21 2017
%Y A133092 Cf. A133091, A000384.
%K A133092 nonn,easy
%O A133092 1,2
%A A133092 _Gary W. Adamson_, Sep 09 2007
%E A133092 Corrected and extended by _Philippe Deléham_, Mar 02 2012