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Search: id:A086754
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| A086754 |
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Pascal's square pyramid read by slices, each slice being read by rows. Each entry in slice n is the sum of the 4 entries above it in slice n-1. |
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| 1, 1, 1, 1, 1, 1, 2, 1, 2, 4, 2, 1, 2, 1, 1, 3, 3, 1, 3, 9, 9, 3, 3, 9, 9, 3, 1, 3, 3, 1, 1, 4, 6, 4, 1, 4, 16, 24, 16, 4, 6, 24, 36, 24, 6, 4, 16, 24, 16, 4, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 5, 25, 50, 50, 25, 5, 10, 50, 100, 100, 50, 10, 10, 50, 100, 100, 50, 10, 5, 25, 50, 50, 25, 5, 1, 5, 10
(list; graph; listen)
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OFFSET
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1,7
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EXAMPLE
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The first 4 slices are
1.11.121.1331
..11.242.3993
.....121.3993
.........1331
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MAPLE
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p:=n->seq(seq(binomial(n, i)*binomial(n, j), j=0..n), i=0..n): seq(p(n), n=0..5); (Deutsch)
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PROGRAM
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(PARI) { pt=vector(10, i, matrix(i, i, j, j, 1)); for (i=3, 10, for (j=2, i-1, pt[i][j, 1]=pt[i-1][j-1, 1]+pt[i-1][j, 1]; pt[i][1, j]=pt[i][j, 1]; pt[i][i, j]=pt[i][j, 1]; pt[i][j, i]=pt[i][j, 1]; ); for(j=2, i-1, for (k=2, i-1, pt[i][j, k]=pt[i-1][j, k]+pt[i-1][j, k-1]+pt[i-1][j-1, k]+pt[i-1][j-1, k-1]))); pt }
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CROSSREFS
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Consider the sequence s[i,j](n) obtained by considering the (i,j)-th entry of the n-th slice. Then if [i,j]= [3,2] we get A006002, if [3,3] we get A000537, if [4,2] we get A004320, if [4,3] we get A004282.
Cf. A046816.
Sequence in context: A105619 A121439 A009205 this_sequence A120880 A059151 A059149
Adjacent sequences: A086751 A086752 A086753 this_sequence A086755 A086756 A086757
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KEYWORD
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nonn,easy
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jul 31 2003
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Nov 18 2004
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