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 A327993 #10 Mar 04 2024 00:43:20
%S A327993 1,3,7,20,55,151,414,1133,3099,8472,23155,63275,172894,472393,1290663,
%T A327993 3526256,9634071,26321031,71910814,196464677,536752579,1466437096,
%U A327993 4006383531,10945648019,29904074046,81699461841,223207100431,609813170912,1666040617711,4551707698639
%N A327993 a(n) = [x^n] ((x - 1)*(x + 1)*(2*x^2 - 1))/(2*x^4 + 4*x^3 - x^2 - 3*x + 1).
%C A327993 a(n) is the sum of row n of A327992 if the decimal digits of A327992(n, k) are read as the binary digits of an integer.
%H A327993 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (3, 1, -4, -2).
%F A327993 a(n) = 3*a(n-1) + a(n-2) - 4*a(n-3) - 2*a(n-4) for n >= 4.
%e A327993 a(6) = 414 = Sum([19, 21, 25, 47, 55, 59, 61, 127]) where the summands correspond to row 6 of A327992: [11001, 10101, 10011, 111101, 111011, 110111, 101111, 1111111].
%p A327993 gf := ((x - 1)*(x + 1)*(2*x^2 - 1))/(2*x^4 + 4*x^3 - x^2 - 3*x + 1):
%p A327993 ser := series(gf, x, 32): seq((coeff(ser, x, n)), n=0..29);
%t A327993 LinearRecurrence[{3, 1, -4, -2}, {1, 3, 7, 20, 55}, 30]
%o A327993 (SageMath)
%o A327993 @cached_function
%o A327993 def a(n):
%o A327993 if n < 5: return [1, 3, 7, 20, 55][n]
%o A327993 return -2*a(n-4) - 4*a(n-3) + a(n-2) + 3*a(n-1)
%o A327993 print([a(n) for n in (0..29)])
%Y A327993 Cf. A327992.
%K A327993 nonn
%O A327993 0,2
%A A327993 _Peter Luschny_, Oct 13 2019