|
%I
%S 1,8,37,129,376,967,2267,4950,10220,20175,38403,70954,127921,226007,
%T 392688,672959,1140260,1914166,3189022,5280288,8699540,14275838,
%U 23352118,38102976,62048869,100888126,163843187,265838881
%N Partial sums of A053295.
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.
%F a(n)=sum{C(n+7-i, n-2i; i=0 to [n/2]}; n >= 0; [x]=greatest integer in x.
%F a(n)=Sum_{k=1..n}{C(n-k+7,k+6)}, with n>=0 - _Paolo P. Lava_, Apr 16 2008
%e a(n)=a(n-1)+a(n-2)+C(n+6,6); n >= 0; a(-1)=0.
%t lst={}; s0=s1=s2=s3=s4=s5=s6=0; Do[s0+=a[n]; s1+=s0; s2+=s1; s3+=s2; s4+=s3; s5+=s4; s6+=s5; AppendTo[lst, s6], {n, 0, 6!}]; lst [From _Vladimir Joseph Stephan Orlovsky_, Dec 10 2008]
%Y Cf. A053739, A014166 and A000045.
%Y Right-hand column 14 of triangle A011794.
%K easy,nonn
%O 0,2
%A Barry E. Williams, Mar 04 2000
|
