

A112358


The following triangle is based on Pascal's triangle. The rth term of the nth row is sum of C(n,r) successive integers so that the sum of all the terms of the row is (2^n)*(2^n+1)/2, the 2^n th triangular number. Sequence contains the triangle read by rows.


2



1, 1, 2, 1, 5, 4, 1, 9, 18, 8, 1, 14, 51, 54, 16, 1, 20, 115, 215, 145, 32, 1, 27, 225, 650, 750, 363, 64, 1, 35, 399, 1645, 2870, 2310, 868, 128, 1, 44, 658, 3668, 8995, 10724, 6538, 2012, 256, 1, 54, 1026, 7434, 24381, 40257, 35658, 17442, 4563, 512, 1, 65
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OFFSET

0,3


COMMENTS

The leading diagonal contains 2^n.
Triangle begins:
1
1 2
1 5 4
1 9 18 8
1 14 51 54 16
...


LINKS

Table of n, a(n) for n=0..56.


FORMULA

T(n,0) = 1, T(n,k) = C(A008949(n,k)+1, 2)  C(A008949(n,k1)+1, 2) = C(n,k)*(A008949(n+1,k)+1)/2 for k>0.  Franklin T. AdamsWatters, Sep 27 2006


EXAMPLE

Row for n = 3 is 1, (2+3+4), (5+6+7), 8.


CROSSREFS

Cf. A112356, A112357, A112359.
Cf. A008949.
Sequence in context: A274105 A056242 A128718 * A126351 A157011 A246173
Adjacent sequences: A112355 A112356 A112357 * A112359 A112360 A112361


KEYWORD

easy,nonn,tabl


AUTHOR

Amarnath Murthy, Sep 05 2005


EXTENSIONS

More terms from Amber Reardon (alr5041(AT)psu.edu) and Vincent M. DelPrince (vmd5003(AT)psu.edu), Oct 04 2005


STATUS

approved



