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A014162
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Apply partial sum operator thrice to Fibonacci numbers.
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7
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0, 1, 4, 11, 25, 51, 97, 176, 309, 530, 894, 1490, 2462, 4043, 6610, 10773, 17519, 28445, 46135, 74770, 121115, 196116, 317484, 513876, 831660, 1345861, 2177872, 3524111, 5702389, 9226935, 14929789
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| With offset 4, number of 132-avoiding two-stack sortable permutations which contain exactly one subsequence of type 51234.
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LINKS
| E. S. Egge and T. Mansour, 132-avoiding two-stack sortable permutations....
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FORMULA
| a(n)=sum(k=0, n, A000045(n-k)*k*(k+1)/2) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 06 2003
G.f.: x/[(1-x)^3(1-x-x^2)].
a(n-2)=sum{k=0..floor(n/2)), binomial(n-k, k+3)}; a(n-2)=sum{k=0..n, binomial(k, n-k+3)}. - Paul Barry (pbarry(AT)wit.ie), Oct 07 2004
Convolution of A000045 and A000217 (Fibonacci and triangular numbers) - Ross La Haye (rlahaye(AT)new.rr.com), Nov 08 2004
Fib(n+6) - (1/2)(n^2+7n+16).
a(n)=Sum_{k=1..n}{C(n-k+3,k+2)}, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Apr 16 2008
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MATHEMATICA
| lst={}; s0=s1=s2=0; Do[s0+=a[n]; s1+=s0; s2+=s1; AppendTo[lst, s2], {n, 0, 6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 10 2008]
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CROSSREFS
| Cf. A000045.
Cf. A001924.
Right-hand column 6 of triangle A011794.
Sequence in context: A193912 A136395 A014160 * A014169 A113684 A014173
Adjacent sequences: A014159 A014160 A014161 * A014163 A014164 A014165
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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