A146881 - OEIS

%I #2 Mar 30 2012 17:34:27

%S 1,1,1,1,8,1,1,11,11,1,1,6,12,6,1,1,9,16,16,9,1,1,12,23,22,23,12,1,1,

%T 15,25,43,43,25,15,1,1,10,30,58,76,58,30,10,1,1,13,38,86,132,132,86,

%U 38,13,1,1,16,49,122,216,254,216,122,49,16,1

%N A symmetrical triangle sequence of coefficients : p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].

%C Row sums are:{1, 2, 10, 24, 26, 52, 94, 168, 274, 540, 1062}.

%F p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; t(n,m)=coefficients(p(x,n)).

%e {1}, {1, 1}, {1, 8, 1}, {1, 11, 11, 1}, {1, 6, 12, 6, 1}, {1, 9, 16, 16, 9, 1}, {1, 12, 23, 22, 23, 12, 1}, {1, 15, 25, 43, 43, 25, 15, 1}, {1, 10, 30, 58, 76, 58, 30, 10, 1}, {1, 13, 38, 86, 132, 132, 86, 38, 13, 1}, {1, 16, 49, 122, 216, 254, 216, 122, 49, 16, 1}

%t Clear[p, x, n]; p[x_, n_] = If[ n == 0, 1, (x + 1)^n +Sum[(1 + Mod[Binomial[n, m], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]]; Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 0, 10}]; Flatten[%]

%K nonn

%O 0,5

%A _Roger L. Bagula_, Nov 02 2008