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1, 13, 36, 60, 84, 108, 132, 156, 180, 204, 228, 252, 276, 300, 324, 348, 372, 396, 420, 444, 468, 492, 516, 540, 564, 588, 612, 636, 660, 684, 708, 732, 756, 780, 804
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For more information, cross-references etc., see A101104.
For n>=3, a(n) is equal to the number of functions f:{1,2,3,4}->{1,2, ...,n} such that Im(f) contains 3 fixed elements. - Aleksandar M. Janjic and Milan R. Janjic (agnus(AT)blic.net), Mar 08 2007
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| a(n)= +2*a(n-1) -a(n-2), n>4.
G.f.: x*(1+x)*(x^2+10*x+1)/(x-1)^2.
a(n) = 24*n-36, n>=3.
a(n) = sum_{j=0..n} (-1)^j*binomial(3, j)*(n - j)^4. [Indices shifted, Nov 01 2010]
a(n) = sum_{i=1..4} A008292(4,i)*binomial(n- i+1,1). [Indices shifted, Nov 01 2010]
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MATHEMATICA
| MagicNKZ=Sum[(-1)^j*Binomial[n+1-z, j]*(k-j+1)^n, {j, 0, k+1}]; Table[MagicNKZ, {n, 4, 4}, {z, 2, 2}, {k, 0, 34}] OR SeriesAtLevelR = Sum[Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; Table[SeriesAtLevelR, {n, 4, 4}, {r, -3, -3}, {x, 3, 35}]
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CROSSREFS
| Cf. A073762.
Sequence in context: A183309 A034119 A054285 * A051865 A081928 A034129
Adjacent sequences: A101100 A101101 A101102 * A101104 A101105 A101106
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KEYWORD
| easy,nonn
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AUTHOR
| Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
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EXTENSIONS
| Removed redundant information already in A101104. Reduced formulas by expansion of constants - R. J. Mathar (mathar(AT)strw.leidenuniv.nl, Nov 01 2010
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