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A086754 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. 2
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; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

Table of n, a(n) for n=1..88.

EXAMPLE

The first 4 slices are

1.11.121.1331

..11.242.3993

.....121.3993

.........1331

MAPLE

p:=n->seq(seq(binomial(n, i)*binomial(n, j), j=0..n), i=0..n): seq(p(n), n=0..5); # Emeric Deutsch, Nov 18 2004

PROG

(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 }

(Haskell)

a086754 n = a086754_list !! (n-1)

a086754_list = concat $ concat $ iterate ([[1, 1], [1, 1]] *) [1]

instance Num a => Num [a] where

   fromInteger k = [fromInteger k]

   (p:ps) + (q:qs) = p + q : ps + qs

   ps + qs         = ps ++ qs

   (p:ps) * qs'@(q:qs) = p * q : ps * qs' + [p] * qs

   _ * _               = []

-- Reinhard Zumkeller, Apr 02 2011

CROSSREFS

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: A307448 A305350 A009205 * A120880 A059151 A290091

Adjacent sequences:  A086751 A086752 A086753 * A086755 A086756 A086757

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Jul 31 2003

EXTENSIONS

More terms from Emeric Deutsch, Nov 18 2004

STATUS

approved

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Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)