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A121547
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Fourth slice along the 1-2-plane in the cube a(m,n,o) = a(m-1,n,o)+a(m,n-1,o)+a(m,n,o-1) for which the first slice is Pascal's triangle (slice read by anti-diagonals).
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0, 0, 1, 0, 4, 4, 0, 10, 20, 10, 0, 20, 60, 60, 20, 0, 35, 140, 210, 140, 35, 0, 56, 280, 560, 560, 280, 56, 0, 84, 504, 1260, 1680, 1260, 504, 84, 0, 120, 840, 2520, 4200, 4200, 2520, 840, 120, 0, 165, 1320, 4620, 9240, 11550, 9240, 4620, 1320, 165, 1980, 7920
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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FORMULA
| a(m-1,n,o)+a(m,n-1,o)+a(m,n,o-1) with initialization values a(1,0,0)=1 and a(m<>1=0,n>=0,0>=o)=0.
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EXAMPLE
| The second row is 1,4,10,20,35,56,84,120,165,220 = A000292 Tetrahedral (or pyramidal) numbers: C(n+2,3) = n(n+1)(n+2)/6 (core).
The third row is 4,20,60,140,280,504,840,1320,1980,2860 = A033488 = n*(n+1)*(n+2)*(n+3)/6.
The main diagonal is 0,4,60,560,4200,27720,168168,960960,5250960,27713400 = unknown.
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PROG
| Excel cell formula: =ZS(-1)+Z(-1)S+Z(-15)S where the term Z(-15)S refers to a cell in the previous slice (along the dimension 3), i.e. Z(-15)S corresponds to +a(m, n, o-1).
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CROSSREFS
| Cf. A003506, A094305, A121306, A119800, A000292, A007318.
Sequence in context: A129507 A021698 A199739 * A028626 A205507 A137862
Adjacent sequences: A121544 A121545 A121546 * A121548 A121549 A121550
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KEYWORD
| nonn,tabl
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AUTHOR
| Thomas Wieder (thomas.wieder(AT)t-online.de), Aug 06 2006
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