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A050407
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n*(n^2-6*n+11)/6.
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5
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0, 1, 1, 1, 2, 5, 11, 21, 36, 57, 85, 121, 166, 221, 287, 365, 456, 561, 681, 817, 970, 1141, 1331, 1541, 1772, 2025, 2301, 2601, 2926, 3277, 3655, 4061, 4496, 4961, 5457, 5985, 6546, 7141, 7771, 8437, 9140, 9881, 10661, 11481, 12342, 13245, 14191
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Number of invertible shuffles of n-2 cards. - Adam C. McDougall (mcdougal(AT)stolaf.edu) and David Molnar )molnar(AT)stolaf.edu), Apr 09, 2002
If Y is a 3-subset of an n-set X then, for n>=3, a(n-2) is the number of (n-3)-subsets of X which have neither one element nor two elements in common with Y. - Milan R. Janjic (agnus(AT)blic.net), Dec 28 2007
Let A be the Hessenberg n by n matrix defined by: A[1,j]=j mod 2, A[i,i]:=1, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=4, a(n+1)=-coeff(charpoly(A,x),x^(n-3)). [From Milan R. Janjic (agnus(AT)blic.net), Jan 24 2010]
Starting with offset 3: (1, 2, 5, 11, 21,...) = triangle A144257 * [1,2,3,...]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 18 2010]
(1 + 2x + 5x^2 + 11x^3 + ...) = (1 + 2x + 3x^2 + ...)*(1 + 2x^2 + 3x^3 + ...). [From Gary W. Adamson (qntmpktk(AT)yahoo.com), Jul 26 2010]
Starting (1, 2, 5, 11,...) = binomial transform of [1, 1, 2, 1, 0, 0, 0,...] [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 25 2010]
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REFERENCES
| R. DiSario, Problem 10931, Amer. Math. Monthly, 109 (No. 3, 2002), 298.
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FORMULA
| Diagonal sums of square array A086460 (starting 1, 1, 2, ...). a(n+2)=1+n(n+1)(n-1)/6=sum{k=0..n, 0^k+(n-k)k}. - Paul Barry (pbarry(AT)wit.ie), Jul 21 2003
binomial(n,3)+binomial(n,0), n>=-1. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006
a(n)=C(n+3,n)+1,n>=-4 . - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2008
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MAPLE
| [seq(binomial(n, 3)+binomial(n, 0), n=-1..46)]; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 24 2006
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MATHEMATICA
| a[n_]:=n*(n^2-6*n+11)/6; ...and/or...a=1; lst={0, 1, 1, a}; k=1; e=1; Do[a+=k; AppendTo[lst, a]; e++; k+=e, {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 17 2008]
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CROSSREFS
| Apart from initial terms, one more than the tetrahedral numbers A000292.
A144257 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 18 2010]
Sequence in context: A022908 A026390 A005575 * A113032 A100134 A137356
Adjacent sequences: A050404 A050405 A050406 * A050408 A050409 A050410
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KEYWORD
| easy,nonn
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AUTHOR
| Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 22 1999
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