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 A139031 #19 Jun 25 2025 10:26:09 %S A139031 3,24,117,336,-237,-10296,-76443,-354144,-922077,1476984,34867797, %T A139031 242017776,1064447283,2465133864,-6890111163,-116749235904, %U A139031 -761741108157,-3175197967656,-6358056037323,28515500892816,387075408075603,2383715742284424,9392840736385317,15549832333971936 %N A139031 Imaginary part of (4 + 3i)^n. %C A139031 Division of each term by 3 generates an integer sequence 1, 8, 39, 112, -79, -3432, -25481, -118048, -307359, 492328, ... - _R. J. Mathar_, Apr 08 2008 %H A139031 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-25). %F A139031 Imaginary part of (4 + 3i)^n. %F A139031 Term (2,1) of [4,-3; 3,4]^n. %F A139031 a(n)^2 + A139030(n)^2 = 5^(2*n). %F A139031 a(n) = 8*a(n-1) - 25*a(n-2), n>2, given a(1) = 3, a(2) = 24. %F A139031 (unsigned): Odd-indexed terms of A066771 interleaved with even-indexed terms of A066776. %F A139031 O.g.f.: 3*x/(1-8*x+25*x^2). - _R. J. Mathar_, Apr 08 2008 %e A139031 a(3) = 117 since (4 + 3i)^3 = (-44 + 117i). %e A139031 a(4) = 336 = 8*a(3) - 25*a(2) = 8*117 - 25*24. %e A139031 a(3) = 117 = term (2,1) of [4,-3; 3,4]^3. %t A139031 a[n_]:=Im[(4+3I)^n];Array[a,24] (* _James C. McMahon_, Jun 25 2025 *) %o A139031 (PARI) a(n) = imag((4 + 3*I)^n); \\ _Michel Marcus_, Jun 25 2025 %Y A139031 Cf. A139030, A066771, A066776. %K A139031 sign,easy %O A139031 1,1 %A A139031 _Gary W. Adamson_, Apr 06 2008