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A053296 Partial sums of A053295. 8


%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.

%H <a href="/index/Rec#order_09">Index to sequences with linear recurrences with constant coefficients</a>, signature (8,-27,49,-49,21,7,-13,6,-1).

%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.

%Y Cf. A228074.

%K easy,nonn

%O 0,2

%A Barry E. Williams, Mar 04 2000

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Last modified December 22 17:45 EST 2014. Contains 252365 sequences.