A071646 - OEIS

%I #11 Nov 07 2013 03:30:52

%S 1,2,6,19,61,201,672,2269,7723,26452,91058,314766,1091884,3798900,

%T 13251136,46325285,162268775,569385098,2001012474,7042014879,

%U 24813529581,87533417037,309107111536,1092585807044,3865270781236

%N Number of base 4 n-digit numbers with digit sum n.

%F a(n)=[x^n] (1+x+x^2+x^3)^n-(1+x+x^2+x^3)^(n-1). - _Michael Somos_, Jul 19 2002

%F a(n)*790*(2*n^2-n) = a(n-1)*(-16328*n^4+137200*n^3-400977*n^2+489925*n-207450)+a(n-2)*(44902*n^4-399751*n^3+1267117*n^2-1672482*n+769980)+a(n-3)*4*(n-3)*(8164*n^3-52272*n^2+115397*n-81223)+a(n-4)*16*(n-4)*(n-3)*(4082*n^2-11849*n+8529), n>2. - _Michael Somos_, Jul 19 2002

%F a(n) = sum(k=1..n, (sum(j=0..k, binomial(j,n-3*k+2*j) *binomial(k,j))) *binomial(n-1,n-k)). [_Vladimir Kruchinin_, Nov 07 2013]

%o (PARI) a(n)=local(y=(x^4-1)/(x-1)); if(n<0,0,polcoeff(y^n-y^(n-1),n))

%o (Maxima) a(n):=sum((sum(binomial(j,n-3*k+2*j)*binomial(k,j),j,0,k))*binomial(n-1,n-k),k,1,n); /* _Vladimir Kruchinin_, Nov 07 2013 */

%Y Cf. A071976, A005773.

%K nonn,base

%O 1,2

%A _John W. Layman_, Jun 22 2002