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A243860 a(n) = 2^(n+1) - (n-1)^2.

%I A243860 #23 Jan 14 2023 16:51:48
%S A243860 1,4,7,12,23,48,103,220,463,960,1967,3996,8071,16240,32599,65340,
%T A243860 130847,261888,523999,1048252,2096791,4193904,8388167,16776732,
%U A243860 33553903,67108288,134217103,268434780,536870183,1073741040,2147482807,4294966396,8589933631,17179868160,34359737279,68719475580
%N A243860 a(n) = 2^(n+1) - (n-1)^2.
%C A243860 Sequences of the form (k-1)^m - m^(k+1):
%C A243860 k\m | 0 |  1 |     2 |       3 |         4 |          5 |           6 |
%C A243860 -----------------------------------------------------------------------
%C A243860 0   | 1 | -2 |    -1 |      -4 |        -3 |         -6 |          -5 |
%C A243860 1   | 1 | -1 |    -4 |      -9 |       -16 |        -25 |         -36 |
%C A243860 2   | 1 |  0 |    -7 |     -26 |       -63 |       -124 |        -215 |
%C A243860 3   | 1 |  1 |   -12 |     -73 |      -240 |       -593 |       -1232 |
%C A243860 4   | 1 |  2 |   -23 |    -216 |      -943 |      -2882 |       -7047 |
%C A243860 5   | 1 |  3 |   -43 |    -665 |     -3840 |     -14601 |      -42560 |
%C A243860 6   | 1 |  4 |  -103 |   -2062 |    -15759 |     -75000 |     -264311 |
%C A243860 7   | 1 |  5 |  -220 |   -6345 |    -64240 |    -382849 |    -1632960 |
%C A243860 8   | 1 |  6 |  -463 |  -19340 |   -259743 |   -1936318 |    -9960047 |
%C A243860 9   | 1 |  7 |  -960 |  -58537 |  -1044480 |   -9732857 |   -60204032 |
%C A243860 10  | 1 |  8 | -1967 | -176418 |  -4187743 |  -48769076 |  -362265615 |
%C A243860 11  | 1 |  9 | -3996 | -530441 | -16767216 | -244040625 | -2175782336 |
%H A243860 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F A243860 a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4). - _Colin Barker_, Jun 12 2014
%F A243860 G.f.: (6*x^3-4*x^2-x+1) / ((x-1)^3*(2*x-1)). - _Colin Barker_, Jun 12 2014
%e A243860 1 = 2^(0+1) - (0-1)^2, 4 = 2^(1+1) - (1-1)^2, 7 = 2^(2+1) - (2-1)^2.
%p A243860 A243860:=n->2^(n + 1) - (n - 1)^2; seq(A243860(n), n=0..30); # _Wesley Ivan Hurt_, Jun 12 2014
%t A243860 Table[2^(n + 1) - (n - 1)^2, {n, 0, 30}] (* _Wesley Ivan Hurt_, Jun 12 2014 *)
%t A243860 LinearRecurrence[{5,-9,7,-2},{1,4,7,12},40] (* _Harvey P. Dale_, Nov 29 2015 *)
%o A243860 (Magma) [2^(n+1) - (n-1)^2: n in [0..35]];
%o A243860 (PARI) Vec((6*x^3-4*x^2-x+1)/((x-1)^3*(2*x-1)) + O(x^100)) \\ _Colin Barker_, Jun 12 2014
%Y A243860 Sequences of the form (k-1)^m - m^(k+1): A000012 (m = 0), A023444 (m = 1), (-1)*(this sequence) for m = 2, A114285 (k = 0),(A000007-A000290) for k = 1, A024001 (k = 2), A024014 (k = 3), A024028 (k = 4), A024042 (k = 5), A024056 (k = 6), A024070 (k = 7), A024084 (k = 8), A024098 (k = 9), A024112 (k = 10), A024126 (k = 11).
%K A243860 nonn,easy
%O A243860 0,2
%A A243860 _Juri-Stepan Gerasimov_, Jun 12 2014