A104747 - OEIS

%I #30 Sep 20 2017 10:56:48

%S 1,4,12,33,87,222,550,1327,3129,7236,16464,36957,82027,180346,393354,

%T 852123,1835181,3932352,8388820,17826025,37748991,79692054,167772462,

%U 352321863,738197857,1543504252,3221225880,6710886837

%N a(n) = (n-3)*2^n + n*(n+3)/2 + 3.

%C Antidiagonal sums of A104746.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (7,-19,25,-16,4).

%F a(n) = +7*a(n-1) -19*a(n-2) +25*a(n-3) -16*a(n-4) +4*a(n-5). G.f. -x*(1-3*x+3*x^2) / ( (2*x-1)^2*(x-1)^3 ). - _R. J. Mathar_, Oct 30 2011

%F a(n) = Sum_{i=0..n-1} (2^(n-i) - 1)*(2^i - i). - _J. M. Bergot_, Sep 13 2017

%F a(n) = Sum_{k=0..n} Sum_{i=1..n} (i-k) * C(n-k,i). - _Wesley Ivan Hurt_, Sep 19 2017

%e First few antidiagonals of A104746 are:

%e 1;

%e 1, 3;  # Row sum 4

%e 1, 4, 7;  # Row sum 12

%e 1, 5, 12, 15;  # Row sum 33

%e 1, 6, 17, 32, 31;

%e 1, 7, 22, 49, 80, 63;

%e ...

%o (PARI) a(n) = (n-3)*2^n + n*(n+3)/2 + 3; \\ _Altug Alkan_, Sep 14 2017

%Y Cf. A104746.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Mar 23 2005