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A112358
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The following triangle is based on Pascal's triangle. The r-th term of the n-th 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.
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2
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The leading diagonal contains 2^n.
Triangle begins:
1
1 2
1 5 4
1 9 18 8
1 14 51 54 16
...
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FORMULA
| T(n,0) = 1, T(n,k) = C(A008949(n,k)+1, 2) - C(A008949(n,k-1)+1, 2) = C(n,k)*(A008949(n+1,k)+1)/2 for k>0. - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 27 2006
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EXAMPLE
| Row for n = 3 is 1, (2+3+4), (5+6+7), 8.
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CROSSREFS
| Cf. A112356, A112357, A112359.
Cf. A008949.
Sequence in context: A194682 A056242 A128718 * A126351 A157011 A092821
Adjacent sequences: A112355 A112356 A112357 * A112359 A112360 A112361
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 05 2005
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EXTENSIONS
| More terms from Amber Reardon (alr5041(AT)psu.edu) and Vincent M. DelPrince (vmd5003(AT)psu.edu), Oct 04 2005
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